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Cohomology of Sheaves

  • Birger Iversen

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Birger Iversen
    Pages 1-73
  3. Birger Iversen
    Pages 74-145
  4. Birger Iversen
    Pages 146-201
  5. Birger Iversen
    Pages 202-253
  6. Birger Iversen
    Pages 254-288
  7. Birger Iversen
    Pages 289-312
  8. Birger Iversen
    Pages 313-331
  9. Birger Iversen
    Pages 332-373
  10. Birger Iversen
    Pages 374-399
  11. Birger Iversen
    Pages 400-423
  12. Birger Iversen
    Pages 424-460
  13. Back Matter
    Pages 461-466

About this book

Introduction

This text exposes the basic features of cohomology of sheaves and its applications. The general theory of sheaves is very limited and no essential result is obtainable without turn­ ing to particular classes of topological spaces. The most satis­ factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon­ strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.

Keywords

Characteristic class Chern class Homotopy cohomology homological algebra homology homotopy theory

Authors and affiliations

  • Birger Iversen
    • 1
  1. 1.Mathematisk InstitutAarhus UniversitetAarhus CDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-82783-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1986
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-16389-3
  • Online ISBN 978-3-642-82783-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site