Intersection Cohomology

ISBN-13: 9780817647643 / Angielski / Miękka / 2008 / 234 str.

Armand Borel

Opis

This volume contains the Notes of a seminar on Intersection Ho- logy which met weekly during the Spring 1983 at the University of Bern, Switzerland. Its main purpose was to give an introduction to the pie- wise linear and sheaf theoretic aspects of the theory Goresky and R. MacPherson, Topology 19(1980) 135-162, Inv. Math. 72(1983) 17-130) and to some of its applications, for an audience assumed to have some familiarity with algebraic topology and sheaf theory. These Notes can be divided roughly into three parts. The first one to is chiefly devoted to the piecewise linear version of the theory: In A. Haefliger describes intersection homology in the piecewise linear context; II, by N. Habegger, prepares the transition to the sheaf theoretic point of view and III, by M. Goresky and R. Mac- Pherson, provides an example of computation of intersection homology. The spaces on which intersection homology is defined are assumed to admit topological stratifications with strong local triviality p- perties (cf I or V). Chapter IV, by N. A'Campo, gives some indications on how the existence of such stratifications is proved on complex analytic spaces. The primary goal of V is to describe intersection homology, or rather cohomology, in the framework of sheaf theory and to prove its main basic properties, following the second paper quoted above. Fa- liarity with standard sheaf theory, as in Godement's book, is assumed.

Recenzje

"The volume should be useful to someone interested in acquiring some basic knowledge about the field..." -Mathematical Reviews

Spis treści

Introduction to Piecewise Linear Intersection Homology.-From PL to Sheaf Theory.-A Sample Computation of Intersection Homology.-Pseudomanifold Structures on Complex Analytic Spaces.-Sheaf Theoretic Intersection Cohomology.-Les Foncteurs de la Categorie des Faisceaux Associes a une Application Continue.-Witt Space Cobordism Theory.-Lefschetz Fixed Point Theorem and Intersection Homology.-Problems and Bibliography on Intersection Homology.-References.

Blurb

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