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Cohomology of Sheaves

  • Textbook
  • © 1986

Overview

Authors:
  1. Birger Iversen

    1. Mathematisk Institut, Aarhus Universitet, Aarhus C, Denmark

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Part of the book series: Universitext (UTX)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XI
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  2. Homological Algebra

    • Birger Iversen
    Pages 1-73

  3. Sheaf Theory

    • Birger Iversen
    Pages 74-145

  4. Cohomology with Compact Support

    • Birger Iversen
    Pages 146-201

  5. Cohomology and Analysis

    • Birger Iversen
    Pages 202-253

  6. Duality with Coefficient in a Field

    • Birger Iversen
    Pages 254-288

  7. Poincare Duality with General Coefficients

    • Birger Iversen
    Pages 289-312

  8. Direct Image with Proper Support

    • Birger Iversen
    Pages 313-331

  9. Characteristic Classes

    • Birger Iversen
    Pages 332-373

  10. Borel Moore Homology

    • Birger Iversen
    Pages 374-399

  11. Application to Algebraic Geometry

    • Birger Iversen
    Pages 400-423

  12. Derived Categories

    • Birger Iversen
    Pages 424-460

  13. Back Matter

    Pages 461-466
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematisk Institut, Aarhus Universitet, Aarhus C, Denmark

    Birger Iversen

Bibliographic Information

  • Book Title: Cohomology of Sheaves

  • Authors: Birger Iversen

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-642-82783-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1986

  • Softcover ISBN: 978-3-540-16389-3Published: 01 April 1986

  • eBook ISBN: 978-3-642-82783-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 464

  • Topics: Algebraic Topology

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