Intersection Cohomology

1. Front Matter

   Pages i-x

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2. Introduction to Piecewise Linear Intersection Homology

   • A. Haefliger

   Pages 1-21

3. From PL to Sheaf Theory (Rock to Bach)

   Pages 23-34

4. A Sample Computation of Intersection Homology

   • M. Goresky, R. MacPherson

   Pages 35-39

5. Structures de Pseudovariété sur les Espaces Analytiques Complexes

   • N. A’Campo

   Pages 41-45

6. Sheaf Theoretic Intersection Cohomology

   • A. Borel

   Pages 47-182

7. Les Foncteurs de la Categorie des Faisceaux Associes a Une Application Continue

   • Pierre-P. Grivel

   Pages 183-207

8. Witt Space Cobordism Theory (after P. Siegel)

   • M. Goresky

   Pages 209-214

9. Lefschetz Fixed Point Theorem and Intersection Homology

   • Mark Goresky, Robert MacPherson

   Pages 215-219

10. Problems and Bibliography on Intersection Homology

    • M. Goresky, R. MacPherson

    Pages 221-233

11. Back Matter

    Pages 234-234

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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.

• Algebraic topology
• Verdier duality
• algebra
• cohomology
• cohomology theory
• homology
• perverse sheaves
• topology

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

• Mathematik, ETH-Zentrum, Zurich, Switzerland

  Armand Borel

• The Institute for Advanced Study, School of Mathematics, Princeton, USA

  Armand Borel

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