Intersection cohomology

Armand Borel (auth.)9780817632748, 9780817647643, 0817632743, 0817647643

This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983.

This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). While some familiarity with algebraic topology and sheaf theory is assumed, the notes include a self-contained account of further material on constructibility, derived categories, Verdier duality, biduality, and on stratified spaces, which is used in the second paper but not found in standard texts.

“The volume should be useful to someone interested in acquiring some basic knowledge about the field…” —Mathematical Reviews

Table of contents :
Front Matter….Pages i-x
Introduction to Piecewise Linear Intersection Homology….Pages 1-21
From PL to Sheaf Theory (Rock to Bach)….Pages 23-34
A Sample Computation of Intersection Homology….Pages 35-39
Structures de Pseudovariété sur les Espaces Analytiques Complexes….Pages 41-45
Sheaf Theoretic Intersection Cohomology….Pages 47-182
Les Foncteurs de la Categorie des Faisceaux Associes a Une Application Continue….Pages 183-207
Witt Space Cobordism Theory (after P. Siegel)….Pages 209-214
Lefschetz Fixed Point Theorem and Intersection Homology….Pages 215-219
Problems and Bibliography on Intersection Homology….Pages 221-233
Back Matter….Pages 234-234