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  • © 2003

Topology of Singular Spaces and Constructible Sheaves

Birkhäuser

Authors:

  • A new cohomological approach to constructible sheaves on stratified spaces, which doesn't use the first isotopy lemma of Thom
  • A self-contained approach to Morse theory for constructible sheaves, including a geometric introduction to the theory of characteristic cycles
  • Very general vanishing and Lefschetz theorems of Artin-Grothendieck type in the complex algebraic and analytic context, which apply in particular to intersection (co)homology and perverse sheaves

Part of the book series: Monografie Matematyczne (MONOGRAFIE, volume 63)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
  2. Introduction

    • Jörg Schürmann
    Pages 1-16
  3. Constructible sheaves in geometric categories

    • Jörg Schürmann
    Pages 81-140
  4. Stratification theory and constructible sheaves

    • Jörg Schürmann
    Pages 207-268
  5. Morse theory for constructible sheaves

    • Jörg Schürmann
    Pages 269-373
  6. Vanishing theorems for constructible sheaves

    • Jörg Schürmann
    Pages 375-431
  7. Back Matter

    Pages 433-454

About this book

Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.

Authors and Affiliations

  • Westfälische Wilhelms-Universität, Münster, Germany

    Jörg Schürmann

Bibliographic Information

  • Book Title: Topology of Singular Spaces and Constructible Sheaves

  • Authors: Jörg Schürmann

  • Series Title: Monografie Matematyczne

  • DOI: https://doi.org/10.1007/978-3-0348-8061-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2003

  • Hardcover ISBN: 978-3-7643-2189-5Published: 24 October 2003

  • Softcover ISBN: 978-3-0348-9424-1Published: 30 October 2012

  • eBook ISBN: 978-3-0348-8061-9Published: 06 December 2012

  • Series ISSN: 0077-0507

  • Series E-ISSN: 2297-0274

  • Edition Number: 1

  • Number of Pages: X, 454

  • Topics: Algebraic Topology, Algebraic Geometry, Category Theory, Homological Algebra

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access