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Sheaf Theory

  • Glen E. Bredon

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

Table of contents

  1. Front Matter
    Pages N1-xi
  2. Glen E. Bredon
    Pages 1-32
  3. Glen E. Bredon
    Pages 33-178
  4. Glen E. Bredon
    Pages 179-196
  5. Glen E. Bredon
    Pages 197-278
  6. Glen E. Bredon
    Pages 279-416
  7. Glen E. Bredon
    Pages 417-448
  8. Back Matter
    Pages 449-504

About this book

Introduction

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 impor­ tant 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 con­ cept of the "tautness" of a subspace (an adaptation of an analogous no­ tion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The fact that 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.

Keywords

Algebraic topology Cech cohomology Characteristic class Cohomology De Rham cohomology Homotopy Sheaf cohomology algebra cohomology group fibrations homological algebra homology

Authors and affiliations

  • Glen E. Bredon
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0647-7
  • Copyright Information Springer-Verlag New York, Inc. 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6854-3
  • Online ISBN 978-1-4612-0647-7
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site
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