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Sheaf Theory

  • Textbook
  • © 1997

Overview

Authors:
  1. Glen E. Bredon

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 170)

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Table of contents (6 chapters)

  1. Front Matter

    Pages N1-xi
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  2. Sheaves and Presheaves

    • Glen E. Bredon
    Pages 1-32

  3. Sheaf Cohomology

    • Glen E. Bredon
    Pages 33-178

  4. Comparison with Other Cohomology Theories

    • Glen E. Bredon
    Pages 179-196

  5. Applications of Spectral Sequences

    • Glen E. Bredon
    Pages 197-278

  6. Borel-Moore Homology

    • Glen E. Bredon
    Pages 279-416

  7. Cosheaves and Čech Homology

    • Glen E. Bredon
    Pages 417-448

  8. Back Matter

    Pages 449-504
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Keywords

About this book

This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." Sheaves play several roles in this study. For example, they provide a suitable notion of "general coefficient systems." Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas impor­tant to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the con­cept of the "tautness" of a subspace (an adaptation of an analogous no­tion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The factthat sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a "single space" theory.

Authors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Glen E. Bredon

Bibliographic Information

  • Book Title: Sheaf Theory

  • Authors: Glen E. Bredon

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0647-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-94905-5Published: 24 January 1997

  • Softcover ISBN: 978-1-4612-6854-3Published: 28 September 2012

  • eBook ISBN: 978-1-4612-0647-7Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XI, 504

  • Additional Information: Originally published by McGraw Hill, 1967

  • Topics: Algebra, Algebraic Topology

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