Leray in Edelbach

The Mathematical Tourist Dirk Huylebrouck, Editor

his is a most unlikely place for the on functional analysis in the Siberian Tmathematical tourist to visit. In fact, camp of Nikolsk-Ussurisk, during World Leray in it is off-limits for tourists of any kind. War I; and a century before, the Napo- Photographing, filming, even drawing, leonic officer Jean-Victor Poncelet de- is prohibited by law, as signposts tell veloped projective geometry while in Edelbach you sternly, and trespassers will be Russian captivity for five years. This punished. If they survive at all, that is. may sound as if the monastic reclusion Anna Maria Sigmund, Peter Michor, Indeed, the signposts also warn you of and monotonic regularity of confined and Karl Sigmund LEBENSGEFAHR, meaning mortal life provided ideal conditions for con- danger. You are in a military zone, and centrating the mind. And indeed, An- had better watch out. Don’t step on any dré Weil wrote that “nothing is more mines, and avoid getting shot, says an favourable than prison for the abstract urgent inner voice. sciences” [Weil 1991]. He wrote this But this is ridiculous. We are in Aus- while he was in prison, and managed, tria, after all, with almost sixty years of during his months of captivity, to find peace and prosperity behind us. No- some of his major theorems. But he body wants any trouble. Let’s not get had a prison cell for himself, could re- caught, that’s all. ceive visits from his family, and knew Welcome to Edelbach, or what is assuredly, to use his words, “captivity left of it. The place is not easily found from its most benign side only.” The on a map: it ceased to exist many years physical and psychic deprivations of ago, during the darkest days of Aus- years in a POW camp, with its over- trian history. Nobody lives here any crowding, sickness, hunger, and biting longer. The main road between Vienna cold, on top of the boredom and un- and Prague is a couple of miles to the certainty, were something else: in Does your hometown have any north, but it can be neither seen nor these conditions, intense intellectual mathematical tourist attractions such heard. An eerie silence hangs over the pursuit must have been a desperate as statues, plaques, graves, the café place. All that remains of the former means for keeping hold of sanity. village are a few stone-heaps between The prisoners of Edelbach founded where the famous conjecture was made, thickets of fir trees, and a small, aban- a “University in Captivity.” Of the 5,000 the desk where the famous initials doned graveyard. To the north of it, a inmates of the camp, of which a few are scratched, birthplaces, houses, or modern fence surrounds a vast ammu- hundred were Polish and the rest memorials? Have you encountered nition depot. It is very well guarded, French, almost 500 got degrees, and and you can be sure, by now, that their diplomas were all officially con- a mathematical sight on your travels? binoculars are fixed on you. firmed in France after the war. The fact If so, we invite you to submit to this This place was once a camp for pris- that Jean Leray had been the director, column a picture, a description of its oners of war, mostly French officers. or recteur, of this impromptu univer- mathematical significance, and either An “Offizierslager”—or Oflag for short: sity must have helped with the French the bureaucrats of the Third Reich authorities. His academic credentials a map or directions so that others were fond of abbreviations. Oflag were impressive: he had received his may follow in your tracks. XVIIA was the birthplace of a substan- doctorate at the élite École Normale tial part of algebraic topology. Spectral Supérieure in Paris, and had been pro- sequences and the theory of sheaves fessor at the Université de Nancy before were fathered here by an artillery lieu- being drafted into the war. His joint tenant named Jean Leray, during an in- work with the Polish mathematician ternment lasting from July 1940 to May Juliusz Schauder (later a victim of the 1945 ([Sch 1990][Eke 1999][Gaz 2000]). Holocaust) developed a topological in- Please send all submissions to In the annals of science one finds variant to prove the existence of solu- Mathematical Tourist Editor, several examples of first-rate mathe- tions of partial-differential equations. Dirk Huylebrouck, Aartshertogstraat 42, matical research conducted by prison- This earned him in 1940 the Grand Prix 8400 Oostende, Belgium ers of war. The Austrian Eduard Helly, in mathematics from the Académie des e-mail: [email protected] for instance, wrote a seminal paper Sciences de Paris.

But Leray was not the only distin- public finances, and on astronomy. The pensive house,” before having to return guished scientist in the Oflag. There course on probability was given by to their cheerless cold quarters. The was the embryologist Étienne Wolff, by Lieutenant Jean Ville, who had pub- barracks consisted of two rooms hous- all testimonies a driving force behind lished, just before the war, an inge- ing 100 inmates each, one small kitchen, the university, but obliged, for racial nious elementary proof of von Neu- and one toilet with eight wash-basins. reasons, to keep discreetly in the back- mann’s minimax theorem [Poll 1989]. There was a special building for the ground. Étienne Wolff later became Recteur Leray lectured mostly on cal- showers: each officer could use it professor at the Collège de France, and culus and topology. He had succeeded twice a month. Half of one barrack was member of the Académie des Sciences in hiding from the Germans the fact that used as a chapel. More than seventy of de Paris as well as of the Académie he was a leading expert in fluid dynam- the prisoners were priests, and each Française. Another luminary was ics and mechanics (a mécanicien, as could say mass daily if he wished. The François Ellenberger, a future presi- he liked to say). He turned, instead, to captives founded a first-rate choir and dent of the Société Géologique de algebraic topology, a field which he a theatre group, and soon set up their France. The geologists at Oflag XVII deemed unlikely to spawn war-like ap- own sports stadium, named stade Pé- had to content themselves with the plications. This led, first, to some notes tain. The prisoners even managed to stones they could find in the prison in the Comptes Rendus de l’Académie produce, behind the back of their yard. Their laboratory was an old des Sciences de Paris, and eventually to guards, a documentary film of about kitchen which they could use for a few a three-part work “Algebraic topology thirty minutes’ length, entitled Sous le hours daily. taught in captivity,” which was submit- Manteau (“Beneath the Cloak,” be- Eventually, friends and relatives ted in 1944 to the Journal des Mathé- cause the camera had always to remain from France were permitted to send matiques Pures et Appliquées, through hidden). Three versions of it have sur- books. Over the years, Leray received the good offices of Heinz Hopf from vived to this day ([989][Kus 2004]). a small library from his former teacher neutral Switzerland, who endorsed it As in many other POW camps, the Henri Villat [Sch 1990], [Ell 1948]. enthusiastically. It was published, after captives printed their own newspaper, From eight in the morning to eight Leray’s release, in 1945 [CRAS 1942] a weekly called Le Canard . . . en KG. in the evening, Barrack 19 housed lec- [JMPA 1945]. KG is Wehrmacht shortspeak meaning tures on law and biology, on psychol- The university’s curriculum shows Kriegsgefangener, or prisoner of war, ogy and Arab language, on music and that on Sunday nights, the prisoners and the French would pronounce it as moral theology, on horse-raising (by a could listen to a lecture giving “practi- Le canard encagé (The caged duck), a Polish fellow-officer, bien sûr!), on cal advice for constructing an inex- pun referring to the celebrated Le Ca-

42 THE MATHEMATICAL INTELLIGENCER nard Enchaîné (The duck in chains), not really nearby (some 83 kilometres rate it with twigs and greenery, hiding which was, and still is, a hugely popu- away). Edelbach is closer to Vienna than it partially from the guard towers. Be- lar satirical journal in France. The pris- to Austerlitz, but for the defeated French cause delegates of the International oners’ version was not permitted to officers, the thought of being near the Red Cross had found that the camp comment on politics, satirically or oth- site of the great Napoleonic victory—“à lacked protection against Allied air erwise: it was filled with harmless car- portée de canon d’Austerlitz,” as some raids, the POWs were told to dig a few icatures, theatre bills, sports news, liked to say—must have been a solace. trenches, and were even provided with crossword puzzles, and announce- At first, they all had hoped to be back shovels and wheel-barrows. Under a ments of special lectures. Nothing in France by the end of 1940. The war plank bridging one of the dug-outs, they about the war, or about the conflicts seemed over. When this proved an il- started burrowing in earnest. The tun- dividing the French community into lusion, many fell prey to depression nel grew quickly, by almost a metre per what, with hindsight, was simply the and to homesickness. Leray and his day, although water kept flooding in. issue of collaboration vs. résistance, academic colleagues used to meet After some time, ventilation became a but seemed much more confusing at every evening in the highest, southern- problem: through a hose made from tin the time. The Vichy régime tried to fos- most corner of the camp, and watch, cans, fresh air had to be pumped into ter a network of “hommes de confi- weather permitting, the sunset over “la the gallery, which was less than two ance,” but an underground résistance petite France.” feet wide and three feet high. In paral- group, who called themselves the Needless to say, the French did not lel, a tailor shop produced civilian mafia, eventually became the dominat- merely bemoan their fate. Some tried clothes, and the printing press pre- ing force in the camp. For many of the to change it. The prison guards became pared maps and forged documents. prisoners, the dilemma was whether to experts at discovering tunnel en- Canned food was hoarded in hidden become a civilian worker in Germany, trances beneath the barracks. They depots. with a freedom . . . of sorts, or to stick were so good at it that they overlooked The first group left on a Saturday it out behind the barbed wire, in the a tunnel entrance which was out in the night. Their escape went unnoticed hope that the legal status of a captive open, right under their noses. It was during Sunday, because some of the officer would protect them from the through this 90-meters-long tunnel that guards were on holiday. The second worst. For Leray, who in 1933 had wit- on the nights of September 17 and 18, group left on the following night. Most nessed in Berlin the accession of Hitler 1943, no fewer than 132 prisoners de- of the runaways hoped to pass for to power, collaboration was never an camped. It was the greatest escape French civilians, of whom there were issue. from a POW camp in World War II, and many working in Germany at that time. When Leray later spoke about Edel- its story is almost unknown [Kus 2004]. The first escapees were arrested and bach, he located it “near Austerlitz, in The prisoners had established an returned to the camp by the police Austria” [Sch 1990]. Actually, Austerlitz open-air theatre, called Théâtre de la even before the break-out was discov- is across the border, in Czechia, and Verdure. They were allowed to deco- ered by the military guards. Eventually,

Fig. 2. Lieutenant Jean Leray, POW, became the rector of the “University in Captivity.” The picture on the right shows him with his Edelbach colleagues. Some would later join him at the Sorbonne or the Collège de France [Gaz 2000].

© 2005 Springer ScienceBusiness Media, Inc., Volume 27, Number 2, 2005 43 Fig. 3. The curriculum of the Université en Captivité [Poll 1989]. As Leray later said, “students had no other distraction than their studies. They had little to eat, and little to keep warm; but they were courageous.” [Sch 1990] only two fugitives managed to reach Döllersheim. This was the largest mil- ulations. One of the closest as- France. itary training ground in central Europe, sociates of the Führer, Hans Frank, Soon after, a panel of agitated Ger- twenty kilometres in diameter, larger would later write, in his death cell in man officers, including several gener- than the dukedom of Liechtenstein. Nuremberg, that Hitler intended there- als, visited the Oflag, where they were A few months after the Anschluss, by to erase all traces of his origins filmed surreptitiously by the French Hitler’s annexation of Austria in 1938, [Frank 1953]. He reported that these prisoners. The commission decided to the German army had taken over the traces could reveal a dark secret, the play down the escape—it did not show ground. Forty-five villages with more shame and scandal of the Third Reich: the Wehrmacht in a favourable light. than seven thousand inhabitants were namely, that Hitler had a Jewish grand- The prisoners were sternly told that hastily evacuated, and huge mechanised father. This rumour, which had been they should not try it again. Handbills forces rattled across the fields, taking widespread in Nazi Germany and still were distributed warning that “break- little notice of the fact that the harvest finds adherents today, has been de- ing out is no longer a sport” and that was not yet in. The Wehrmacht had to bunked by scores of historians since. death zones were waiting for the run- live up to its new and as yet untested Hitler’s father had been born out of aways. Half a year later, 76 British fly- doctrine of the Blitzkrieg. The barracks wedlock, as Alois Schicklgruber, and ers escaped from Oflag III Luft in which Leray and his fellow-prisoners was later to change his name, but the Sagan. This time, the Wehrmacht could were soon to use were erected origi- Führer was far too powerful to have felt no longer keep it a secret from Hitler nally to house the first German soldiers threatened by slurs concerning his an- and Himmler. Only three of the fugi- claiming the exercise grounds. Very cestry. In fact, when the villages around tives reached England; 50 were shot. soon, the Truppenübungsplatz proved Döllersheim were evacuated, all church During the five years that Leray an ideal stepping-stone for the armies archives were properly stored. They are spent in Oflag XVII, battles raged from which were assembling to invade and preserved to this day. For years, the one end of Europe to the other, at no dismember nearby Czechoslovakia, in Wehrmacht had been looking for a king- time touching Edelbach. Nevertheless, spring 1939, and for preparing the as- sized training ground to accommodate the booming of great guns and the an- sault on Poland during the following its frantic growth, and to manoeuvre gry buzz of Stukas could be heard at all summer months [Poll 1989]. with its new weapons, whose range times by the inmates of the camp. In- The fact that both the father and the would not fit into existing exercise ar- deed, Oflag XVII was located within mother of Adolf Hitler had been born in eas. The Waldviertel (or woods district), an evacuated zone, strictly off-limits the region, which was so suddenly and with its poor soil and its sparse, lowly for civilians, the Truppenübungsplatz ruthlessly evacuated, gave rise to spec- population was perfectly suited: a hilly

44 THE MATHEMATICAL INTELLIGENCER plateau, some 600 metres above sea sional quarters and the promise of a But during Leray’s years of intern- level, with long, bitterly cold winters, settlement after the war. In 1942, all ment he was daily faced with the and no reputation for hospitality. evacuees were offered a special re- vacant houses of a seemingly intact, It is clear that Hitler had no emo- duction on a richly produced coffee- menschenfrei Edelbach behind the tional ties to the Waldviertel. The prop- table book, Die alte Heimat, complete barbed-wire fence. The chimneys did aganda from the Goebbels ministry had with pictures of their empty villages, and not smoke and the doors never opened. hailed it as the Ahnengau, the cradle of Hitler’s family tree as a keepsake [Heim The window-panes had been replaced the ancestors, and the humble dwellers 1942]. In the ensuing years, Nazi au- by planks. A poem on the front page of of the tiny hamlet of Grosspoppen, led thorities had other things on their minds. the Canard en KG, with the title Le vil- by their inn-keeper, had conferred hon- Eventually, the district of Lower Austria lage ignoré, describes the mute bell- orary citizenship on Hitler in 1932, was occupied by the Red Army, which tower of the deserted hamlet, and the when he was a rising young politician could find good use for the vast training silence broken only by the wind [Poll and demagogue. In return, they first got opportunities filled with bunkers and 1989]. And while the Nazi picture book scolded by the authorities of Lower artillery ranges. By 1955, the Allied oc- acknowledges that when Edelbach had Austria (who pointed out that the ac- cupation troops left Austria, but the to be cleared out, some left it with a tion was legally void because Hitler evacuated region was not returned to bleeding heart, the captive French poet was no longer an Austrian citizen), its former dwellers. They had been imagines how his heart, far from bleed- then frowned upon by the Viennese scattered all over the district and were ing, “jumps with joy on the day, known regime, which was engaged in a hope- far too weak to succeed in their de- only to destiny,” when he is released less struggle against illegal Nazis, and mands for a return. The small new Aus- and the forsaken village vanishes be- finally, right after the revels of the an- trian army managed to keep the over- hind the firs. nexation, expelled from their land sized training grounds for itself. Those The day known only to destiny was without further ado. No account was abandoned houses which were still April 17, 1945. The camp had to be taken of the fact that 220 out of the 220 standing, after the years of Nazi and evacuated because the Red Army was citizens of Grosspoppen had voted for Soviet occupation, including Edelbach, perilously close. The Wehrmacht was the Anschluss. In fact their hamlet, were now flattened in a remarkably by now out of gas and lorries. The which obstructed a planned artillery short time. The Austrian army had in- Blitzkrieg days were over. The prison- range, was the first to become men- herited an amazing amount of ammuni- ers had to march, carrying their be- schenrein (the callous Nazi expression tion, and made a point of spending it lav- longings on their backs. Some of the for “evacuated”) and be knocked down. ishly by shelling the empty settlements. guards used bicycles, and their officers A fortunate few were compensated Today only the church of Döllersheim sat on underfed horses. The trek aimed with hastily built ersatz farms, not too survives: its spire serves as a conve- for Linz, some 128 kilometers away to far away. Others were given provi- nient mark for ranging artillery sights. the west. The group covered, on aver-

Fig. 4. Notes from captivity. KG Jean Leray reports, in this Comptes Rendus note from 1942, that in his present condition, he is unable to guarantee the originality of his results [Gaz 2000].

© 2005 Springer ScienceBusiness Media, Inc., Volume 27, Number 2, 2005 45 Fig. 5. No open university, but a closed universe of 440 530 meters. The camp, and campus, of Oflag XVII housed some 5,000 prisoners. Today, the barracks are gone: in their place one finds concrete, earth-covered ammunition dumps. The village of Edelbach is a rubble of stones covered by a dense forest. age, less than ten kilometres a day, and the interiors of rural chapels. The pris- 1942), and then, in 1947, at the presti- dwindled rapidly in size. The marching oners had to look after their own food; gious Collège de France. In 1953 he was column was long, the forest dense. Un- some managed to get it from old wives elected to the Académie des Sciences derfed François Ellenberger schlepped and barefoot children, in exchange for de Paris (which had made him a cor- a rucksack half his own weight: he had soap, which they had produced in their responding member in 1944). He was insisted on taking along his volumi- camp. By May 10, the column had been showered with prizes: among them, the nous mineralogical notes, a hand-made reduced by half. This was the day the prix Ormoy in 1950, the Feltrinelli prize telescope, and his rock samples, some Wehrmacht surrendered. in 1971, the Lomonosov gold medal in of which had come from the tunnel. He After his liberation, Jean Leray be- 1988 (jointly with Sobolev), and in still found the strength to sketch the came professor, first at the University 1979, the Wolf prize, jointly with André lines of the hills in his notebook, and of Paris (which had appointed him in Weil (who, incidentally, had also been

Fig. 6. A room with a view. The barracks were originally built for the Wehrmacht soldiers claiming the grounds. Fences and watchtowers were added later [Poll 1989].

46 THE MATHEMATICAL INTELLIGENCER Fig. 7. Underground film. These clandestine stills show the escape tunnel, also known as métro pour la liberté. The clandestine movie Sous le drapeau, shot in real time, is a French alternative to Hollywood’s The Great Escape [Corr 1954]. a candidate for that same chair at the dharma (that is to say, he was a con- for what soon became a main item on Collège de France). In an obituary writ- scientious objector) and therefore took Bourbaki’s menu, although he had left ten for Nature, Ivar Ekeland called hair-raising risks to avoid waging war the Bourbaki group in 1935. Leray “the first modern analyst,” and against Hitler. Leray served as a patri- Changing direction seems to have compared him with Weil, “the first otic officer and remained stolidly at his posed no problem for Leray. “The es- modern algebraist” [Eke 1999]. post to the end, during the swift Ger- sential characteristic of my publica- The parallels, which also were man assault and throughout the pro- tions is their diversity,” he later said, stressed by Jean-Michel Kantor [Gaz tracted years of confinement. Whereas simply. “It was my interest in mechan- 2000], are indeed intriguing: the two Weil studied abstract algebraic struc- ics that obliged me to give new devel- men share their year of birth, 1906, and tures and shunned anything even re- opments to mathematical analysis and their year of death, 1998. They both motely smacking of applications or algebraic topology” [Sch 1990]. Indeed, were among the very select few to at- physical intuition, Leray was deeply Leray had been interested in topology tend the École Normale Supérieure, steeped in physics and geometry. This even before the war, but as a tool and both did some of their best work makes all the more remarkable the fact rather than as an end in itself. The ho- in prison. But the differences are even that he switched to algebraic topology motopy invariant now known as the more striking. Weil followed his in the prison camp, and laid the basis Leray-Schauder degree was created in

Fig. 8. Cold feet and frosty advice. Unaware of being filmed, a Wehrmacht delegation decided to keep the news of the escape under wraps. But posters warned the French that henceforth, s’évader n’est plus un sport.

© 2005 Springer ScienceBusiness Media, Inc., Volume 27, Number 2, 2005 47 Fig. 9. The church of Edelbach, in an already deserted village. The poem laments that in the humble church, no bell ever rings. In 1957 the church was flattened by Austrian artillery. order to prove the existence of solu- ical physics, were at the centre of ness of solutions of the initial-value tions to non-linear partial-differential Leray’s work. In 1936, he published a problem for the three-dimensional equations. Such equations, particularly truly pioneering paper investigating Navier-Stokes equations for incom- those which stemmed from mathemat- the existence, uniqueness, and smooth- pressible fluids. He showed, in partic-

Fig. 10. Forty years after. This stone commemorates a visit in 1985 by some former inmates of the Oflag. The French prisoners had their own graveyard in Edelbach, complete with funeral statue.

48 THE MATHEMATICAL INTELLIGENCER ular, that non-stationary solutions for the basic object. This was a lasting would devote a whole book to the role smooth initial data remain smooth for achievement. The Leray-Serre spectral of Planck’s constant in mathematics, a finite time only; beyond this, they sequence of a filtration is still in gen- again in an attempt to understand may only be continued in a weak sense eral use today. Grothendieck would Maslov [Ler 1981]. (giving rise to what are called weak so- also stress the importance of the rela- Leray’s concept of spectral se- lutions nowadays). Leray called such tive point of view in algebraic topology quences appeared first as a compli- solutions turbulent, thereby suggest- [Jack 2004]. cated set of relations among various ing that the onset of turbulence is Soon after his release, Leray found a cohomologies of double complexes. caused by the breakdown of smooth- way to define cohomology with respect They allowed Leray to compute the co- ness. He certainly had good reasons to sheaves, and introduced the spectral homology of compact Lie groups and not to wish the Germans to learn of his sequence of a continuous map, which flag manifolds. Serre used spectral se- work. It is interesting to speculate relates the cohomology of the domain quences, already in their modern form, what he would have done if he had to that of the range and of the fibre. His to determine the dimensions in which been given an opportunity to do scien- original ideas, intended to be as general the higher homotopy groups of the tific work for the Allies. as possible, were still not general n-sphere are not finite, namely n and As it was, he “turned his minor into enough, however, for three young 2n-1. Massey made spectral sequences his major interest” and started working Frenchmen named Henri Cartan, Jean- more easily accessible via the notion of on algebraic topology as an end in it- Louis Koszul, and Jean-Pierre Serre. exact couples. self—Weil-style, as it were. He worked They extended his concepts to obtain Leray himself, after 1950, returned to in great, but not total scientific isola- spectacular applications to analytic partial-differential equations. He stud- tion, avoiding contacts with German spaces and algebraic geometry. In the ied the Cauchy problem, its connection mathematicians. Apart from some late forties, the development became al- with multidimensional complex analy- reprints provided by Heinz Hopf, from most breathless [Gaz 2000]. The two sis, residue theory on complex mani- neutral Switzerland, Leray was cut off Fields medallists of 1954, Serre and Ko- folds, and integral representations. Al- from ongoing research, in particular daira, both based their work on Leray’s gebraic topology became a tool again from contemporary, related work by sheaves and spectral sequences. for Jean Leray. The interlude which Eilenberg and Steenrod, and had to In the hands of Cartan and Oka, had begun in the POW camp of Edel- start from scratch. sheaves became an essential tool for bach, as a kind of camouflage, was As Armand Borel later wrote, the theory of several complex vari- over. But generations of pure mathe- Leray’s original concepts, based on a ables. Weil used sheaf cohomology and maticians would exploit the ideas language of his own making, have been spectral sequences on real manifolds which had germinated in Oflag XVIIA. strongly modified or have not survived to give a lucid proof of de Rham’s the- [BHL 2000]. Leray’s aim was to create orem, generalising the Mayer-Vietoris Acknowledgements something similar to differential forms, sequence from an open cover of two We thank Hofrat Dr. Andreas keeping their multiplicative algebraic sets to one of infinitely many sets. Kusternig for a wealth of information structure, but in a purely topological Godement wrote the definitive treat- on Oflag XVIIA. Jean-Michel Kantor, framework. His cohomology was simi- ment of sheaves and their cohomol- Reinhard Siegmund-Schultze, and Han- lar to that created by Cˇech, and his re- ogy for algebraic topology. Serre and nelore Brandt provided considerable sults did not, as Borel wrote, “seem to Grothendieck adapted the notion of help in preparing this article. go drastically beyond those of main- sheaves for algebraic geometry. Even stream algebraic topology.” But the in- the (still unfinished) theory of motives REFERENCES tention behind them was different: concerns a category of sheaves. The [Eke 1999] Ekeland, I.: Jean Leray (1906– Leray aimed at studying, not only the central problem, on which Voevodsky 1998), Nature 397, 482. topology of a space, but the topology made some recent inroads, is to find [Gaz 2000] Gazette des mathématiciens, Sup- of a representation, i.e., topological in- enough injective resolutions for coho- plément au no. 84, 1–88 is entirely dedicated variants for continuous maps. He took mology to work. With the papers of Ko- to Jean Leray, and includes articles by J. M. as starting point his notes on a course daira and Spencer, and the Habilita- Kantor, Y. Choquet-Bruhat, J. Y. Chemin, H. by Élie Cartan on differential forms, tionsschrift of Hirzebruch [Hirz 1956], Miller, J. Serrin, R. Siegmund-Schultze, A. published in 1935 [Cart 1935]. He sheaf cohomology crossed the French Yger, C. Houzel, and P. Malliavin. aimed to understand cohomology borders. Sato used complex analytic [Sch 1990] Schmidt, M.: Hommes de science, (which he persistently called homol- sheaf cohomology to define hyper- Hermann, Paris. ogy) in a way similar to the de Rham functions as generalised boundary val- [Weil 1991] Weil, A.: Souvenirs d’apprentis- cohomology, with its multiplicative ues of holomorphic functions, and in- sage, Birkhäuser, Basel. structure. vestigated microlocal analysis on the [Ell 1948] Ellenberger, F.: La géologie à l’Oflag From his work with Schauder on cotangent bundle. Sato’s microfunc- XVIIA, Annales Scientifiques de Franche- fixed-point theorems, he was used to tions are more powerful than Hörman- Comté 3, 21–24. the relative viewpoint. He considered der’s wave-front sets, which in turn [Corr 1954] Corre, M.: Défense de photogra- mappings between two spaces as were inspired by Maslov. Later, Leray phier, reportage photographique clandestin

ANNA MARIA SIGMUND PETER MICHOR KARL SIGMUND e-mail: [email protected] Fakultät für Mathematik Fakultät für Mathematik Universität Wien Universität Wien 1090 Vienna 1090 Vienna Austria Austria e-mail: [email protected] e-mail: [email protected]

Anna Maria Sigmund is a historian, whose Peter Michor, a differential-geometer, is a Karl Sigmund has protected Intelligencer best-selling Die Frauen der Nazis has been former director of ESI: the International readers against the danger of forgetting translated into twenty-one languages so Erwin Schrödinger Institute for Mathemati- about Austria, by contributing a series of far. The reader will have inferred that she cal Physics, a center for intellectual ex- compelling articles about its history. In his is married to a mathematician. change between East and West and spare time he is a game-theorist and pro- around the world. He is a proponent of af- fessor. fordable electronic publications.

sur la vie d’un camp de prisonniers francais, [Kus 2003] Kusternig, A.: Grosse Flucht aus mobiles, la théorie des groupes continus et Oflag XVII A(Autriche) dem Oflag XVIIA, Niederösterreich Perspek- les éspaces généralisés, Notes written by J. [Poll 1989] Polleross, F.: 1938 Davor—Danach: tiven 3, 22–25. Leray, Hermann, Paris. Beiträge zur Zeitgeschichte des Waldviertels, [Fr 1953] Frank, H.: Im Angesicht des Galgens, [Jack 2004] Jackson, A.: As if summoned from Horn-Krems. München/Gräfelfing. the void, the life of Alexandre Grothendieck, No- [CRAS 1942] Leray, J.: Comptes rendus de [Heim 1942] Die alte Heimat: Sudetendeutsche tices of the AMS 51, 1038–1056, 1196–1212. l’Académie des Sciences de Paris 214, Verlagsdruckerei, Berlin. [Hirz 1956] Hirzebruch, F.: Neue topologische 781–783, 839–841, 897–899, 938–940. [BHL 2000] Borel, A., Henkin, G.M., and Lax, Methoden in der algebraischen Geometrie, [JMPA 1945] Leray, J.: Course d’algèbre P.D.: Jean Leray (1906–1998), Notices AMS Ergebnisse 9, Springer-Verlag, Berlin. topologique enseigné en captivité, J. Math. 47, 350–359. [Ler 1981] Leray, J.: Langrangian analysis and Pures Appl. 24, 95–167, 169–199, 201–248. [Cart 1935] Cartan, E.: La méthode des repères quantum mechanics, MIT Press, Mass.

50 THE MATHEMATICAL INTELLIGENCER