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Sheaves in Topology

  • Alexandru Dimca

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Alexandru Dimca
    Pages 1-22
  3. Alexandru Dimca
    Pages 23-57
  4. Alexandru Dimca
    Pages 59-79
  5. Alexandru Dimca
    Pages 125-164
  6. Alexandru Dimca
    Pages 165-222
  7. Back Matter
    Pages 223-240

About this book

Introduction

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties).

This introduction to the subject can be regarded as a textbook on "Modern Algebraic Topology'', which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology).

The first five chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of hyperplane arrangements.

Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises.

Keywords

Algebraic topology Monodromy cohomology constructible homology perverse sheaf topology variety

Authors and affiliations

  • Alexandru Dimca
    • 1
  1. 1.Laboratoire J.A. Dieudonné, UMR CNRS 6621Université de Nice Sophia-AntipolisNice Cedex 2France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18868-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20665-1
  • Online ISBN 978-3-642-18868-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site