The Development of Intersection Homology Theory Steven L
Pure and Applied Mathematics Quarterly Volume 3, Number 1 (Special Issue: In honor of Robert MacPherson, Part 3 of 3 ) 225|282, 2007 The Development of Intersection Homology Theory Steven L. Kleiman Contents Foreword 225 1. Preface 226 2. Discovery 227 3. A fortuitous encounter 231 4. The Kazhdan{Lusztig conjecture 235 5. D-modules 238 6. Perverse sheaves 244 7. Purity and decomposition 248 8. Other work and open problems 254 References 260 9. Endnotes 265 References 279 Foreword The ¯rst part of this history is reprinted with permission from \A century of mathematics in America, Part II," Hist. Math., 2, Amer. Math. Soc., 1989, pp. 543{585. Virtually no change has been made to the original text. However, the text has been supplemented by a series of endnotes, collected in the new Received October 9, 2006. 226 Steven L. Kleiman Section 9 and followed by a list of additional references. If a subject in the reprint is elaborated on in an endnote, then the subject is flagged in the margin by the number of the corresponding endnote, and the endnote includes in its heading, between parentheses, the page number or numbers on which the subject appears in the reprint below. 1. Preface Intersection homology theory is a brilliant new tool: a theory of homology groups for a large class of singular spaces, which satis¯es Poincar¶eduality and the KÄunnethformula and, if the spaces are (possibly singular) projective algebraic varieties, then also the two Lefschetz theorems. The theory was discovered in 1974 by Mark Goresky and Robert MacPherson.
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