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Essays on Topology and Related Topics Memoires Dedies a Georges De Rham Semisimpliziale Algebraische T Opologie Essays on Topology and Related Topics Memoires dedies a Georges de Rham Semisimpliziale algebraische T opologie Von K. LAMOTKE, Mathem;ltisdll~S Institut der Universi tat Bonn VIII, 285 Seitl'n. 1965 (Die Grundlehrcn dcr mathematischcn Wissenschaften, Band 147) Gcbundell DM 48,-; US 8 13.20 In dcn ersten b,·iden Kapitcln werden die Grundbcgritfc aus der Tlll'oril' dcr scmi­ simplizialell Mcngen eingcfUhrt. Dabci wird stl'ts die Analogie zu den cntsprc­ chenden Begriffen der Ublichen Topologie betont, um d"1l1 hiermit vertr.lut,'n Leser das Verstandnis zu erk'idltertl. In dl'n folgmden sid)en Kapitcln werdell dil' wes,'ntlichen T l'ile der khssischell algc­ braischell Topologie mit semisimplizi;llen M"thoden entwickclt. Den Anfang bilden die Fundamentalgruppen und die Obcr­ hgerungstheoric (3. Kapitcl). Nach ciner Zusammeniassung dcr notwendigl'll lk­ griffc dcr homologischen Algcbra (4. Ka­ pi tel) folgt il11 5. Kapitcl die (Ko-) HOl11o­ logiethcoric. Hier liegt die scmisimplizialc Darstellung besonders auf der H'lnd, d.l die singularc Homologiethcoric gcschicht­ lich gesehell zur Entwicklung dcr semi­ simplizialen Mengen gcfUhrt hat. Aber auch bl'i den anderen, teilwcise kompli­ zicrtcn Methoden dcr algcbraischcn Topo­ logic gcst.lttct dcr semisimplizialc St.lI1lI­ punkt cine einhl,itlidll'\"l' und mandullal einfachere Darstcllung, als es dic ur­ sprUnglichl're Bl'trachtungswcisc crmog­ lichtI.': Es handelt sich um die Spektral­ sequenz einer Faserung (6. Kapitel), die Homotopicgruppen (7. Kapitel), die Eilen­ bcrg-J\hcLane-Komplcxe und di,' Post­ niko\'zerll'gung (8. Kapitcl), die Kohomo­ logieopl'rationen, insbesondere die Stel'l1- rodschcn reduzil'rtl'n Potenzcn (9. Ka­ pitel). SPRINGER-VERLAG BERLIN· HEIDELBERG' NEW YORK Essays on Topology and Related Topics Memoires dedies a Georges de Rham Publies sous la direction de Andre Haefliger . Raghavan Narasimhan Springer-Verlag Berlin· Heidelberg· New York 1970 ISBN-13: 978-3-642-49199-3 e-ISBN-13: 978-3-642-49197-9 DOl: 10.1007/978-3-642-49197-9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin· Heidelberg 1970. Library of Congress Catalog Card Number 74-96951. Softcover reprint of the hardcover 1st edition 1970 Essays on Topology and Related Topics Memoires dedies a Georges de Rham Publies sous la direction de Andre Haefliger· Raghavan Narasimhan Springer-Verlag New York· Heidelberg· Berlin 1970 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin' Heidelberg 1970. Library of Congress Catalog Card Number 74-96951. Title No. 1629. Georges de Rham est ne Ie 10 Septembre 1903. Un colloque a ete organise a r Universite de Ge­ neve en son honneur les 26, 27 et 28 Mars 1969. Ce volume reunit des articles presentes a cette occasion et des memo ires dedies a Georges de Rham par ses amis et ses eleves. Dear Professors Haefliger and Narasimhan, Personal difficulties prevent me from attending the Colloquium in honour of Georges de Rham. Illustrious mathematicians will speak for the impact of his work, its invincible elegance, and its enduring value. But the distinction of his personality makes him even taller. Tough as steel in his adherence to principle, resilient, placable, self-less and generous beyond the dictates of fashion, steadfast in friendship, but not at the price of reason, de Rham strides the world of mathematics a happy warrior. As President of the International Mathematical Union, he did as much as anyone man could do to bring mathematicians together, young and old, classical and modern, from the East and West. He found a special joy in the spectacle of younger colleagues adding to the old heritage, and did as much as he could to encourage them. He has enriched mathematics by the creations of his mind, and mathematical life by his great human qualities. To honour him for what he has said, for what he has done, and for what he is, is to re­ cognize, in gladness, the unwaning power of our science and the ties that bind its votaries. I wish Georges de Rham many more years of service, for service is the secret of his vitality. With kindest regards, Yours sincerely, Zurich, March 24, 1969 (K. Chandrasekharan) Table of Contents HENRI CARTAN Les travaux de Georges de Rham sur les varietes differentiables JOHN MILNOR and OSCAR BURLET Torsion et type simple d'homotopie 12 MICHAEL ATIYAH and FRIEDRICH HIRZEBRUCH Spin-Manifolds and Group Actions . 18 PAUL F. BAUM and RAOUL BOTT On the Zeroes of Meromorphic Vector-Fields 29 RAOUL BOTT and SHIING S. CHERN Some Formulas Related to Complex Transgression 48 KUNIHIKO KODAIRA On Homotopy K3 Surfaces. 58 ARMAND BOREL Pseudo-concavite et groupes arithmetiques 70 ALDO ANDREOTTI and GIUSEPPE TOMASSINI Some Remarks on Pseudoconcave Manifolds 85 JEAN-LoUIS KOSZUL Trajectoires convexes de groupes affines unimodulaires. 105 EDOARDO VESENTINI Maximum Theorems for Spectra . 111 NICOLAAS H. KUIPER and BESSELINE TERPSTRA-KEPPLER Differentiable Closed Embeddings of Banach Manifolds . 118 MORRIS W. HIRSCH On Invariant Subsets of Hyperbolic Sets. 126 WILLIAM BROWDER and TED PETRIE Semi-Free and Quasi-Free Sl Actions on Homotopy Spheres . 136 S. P. NOVIKOV Pontrjagin Classes, the Fundamental Group and Some Problems of Stable Algebra . 147 x Table of Contents JACQUES BOECHAT et ANDRE HAEFLIGER Plongements differentiables des varietes orientees de dimension 4 dans R7 ........................ 156 CLAUDE WEBER Taming Complexes in the Metastable Range 167 BENO ECKMANN et SERGE MAUMARY Le groupe des types simples d'homotopie sur un polyedre. 173 JACQUES TITS Sur Ie groupe des automorphismes d'un arbre . 188 MICHEL A. KERVAIRE Multiplicateurs de Schur et K-theorie 212 RENETHOM Topologie et linguistique. 226 Liste des publications scientifiques de G. de Rham . 249 List of Contributors ALDO ANDREOTTI Universitil di Pisa, Istituto Matematico, "Leonida Tonelli", Pisa. MICHAEL ATIYAH School of Mathematics, The Institute for Advanced Study, Prince­ ton/NJ. PAUL F. BAUM Department of Mathematics, Brown University, Providence/RI. JACQUES BOECHAT Institut de Mathematique, Universite de Geneve, Geneve. ARMAND BOREL School of Mathematics, The Institute for Advanced Study, Prince­ ton/NJ. RAOUL BOTT Department of Mathematics, Harvard University, Cambridge/MA. WILLIAM BROWDER Department of Mathematics, Princeton University, Princeton/NJ. OSCAR BURLET Institut de Mathematique, Universite de Geneve, Geneve. HENRI CARTAN 95, Boulevard Jourdan, Paris. SHIING S. CHERN Department of Mathematics, University of California, Berkeley/CA. BENO ECKMANN Forschungsinstitut fUr Mathematik der ETH Zurich, Zurich. ANDRE HAEFLIGER Institut de Mathematique, Universite de Geneve, Geneve. MORRIS W. HIRSCH Department of Mathematics, University of California, Berkeley/CA. XII List of Contributors FRIEDRICH HIRZEBRUCH Mathematisches Institut der Universitat Bonn, Bonn. MICHEL A. KERVAIRE Courant Institute of Mathematical Science, New York University, New York/NY. KUNIHIKO KODAIRA Department of Mathematics, University of Tokyo, Hongo, Tokyo. JEAN-LoUIS KOSZUL Departement de Mathematique, Universite de Grenoble, Grenoble. NICOLAAS H. KUIPER Mathematisch Instituut van de Universiteit van Amsterdam, Amsterdam. SERGE MAUMARY School of Mathematics, The Institute for Advanced Study, Prince­ ton/NJ. JOHN MILNOR Massachusetts Institute of Technology, Cambridge/MA. S. P. NOVIKOV Institute AN SSSR, Moscow. TED PETRIE Institute for Defence Analyses, Princeton/NJ. BESSELINE TERPSTRA-KEPPLER Mathematisch Instituut van de Universiteit van Amsterdam, Amsterdam. RENETHOM Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette. JACQUES TITS Mathematisches Institut der Universitat Bonn, Bonn. GIUSEPPE TOMASSINI Universita di Pisa, Istituto Matematico, "Leonida Tonelli", Pisa. EDOARDO VESENTINI Scuola Normale Superiore, Pisa. CLAUDE WEBER Institut de Mathematique, Universite de Geneve, Geneve. .
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