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  • Textbook
  • © 2016

Manifolds, Sheaves, and Cohomology

Authors:

  • Provides a modern introduction to the theory of manifolds
  • Offers a good preparation for more advanced geometric theories
  • A novel approach for master students in mathematics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Studium Mathematik - Master (SSMM)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xvi
  2. Topological Preliminaries

    • Torsten Wedhorn
    Pages 1-20
  3. Algebraic Topological Preliminaries

    • Torsten Wedhorn
    Pages 21-40
  4. Sheaves

    • Torsten Wedhorn
    Pages 41-68
  5. Manifolds

    • Torsten Wedhorn
    Pages 69-90
  6. Linearization of Manifolds

    • Torsten Wedhorn
    Pages 91-121
  7. Lie Groups

    • Torsten Wedhorn
    Pages 123-137
  8. Torsors and Non-abelian \Čech Cohomology

    • Torsten Wedhorn
    Pages 139-151
  9. Bundles

    • Torsten Wedhorn
    Pages 153-192
  10. Soft Sheaves

    • Torsten Wedhorn
    Pages 193-204
  11. Cohomology of Complexes of Sheaves

    • Torsten Wedhorn
    Pages 205-232
  12. Cohomology of Constant Sheaves

    • Torsten Wedhorn
    Pages 233-244
  13. Appendix A: Basic Topology

    • Torsten Wedhorn
    Pages 245-269
  14. Appendix B: The Language of Categories

    • Torsten Wedhorn
    Pages 271-290
  15. Appendix C: Basic Algebra

    • Torsten Wedhorn
    Pages 291-315
  16. Appendix D: Homological Algebra

    • Torsten Wedhorn
    Pages 317-330
  17. Appendix E: Local Analysis

    • Torsten Wedhorn
    Pages 331-340
  18. Back Matter

    Pages 341-354

About this book

This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. 

Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Reviews

“This book is to introduce powerful techniques used in modern Algebraic and Differential Geometry, fundamentally focusing on the relation between local and global properties of geometric objects and on the obstructions to passing from the former to the latter. … The readership for this book will mostly consist of beginner to intermediate graduate students, and it may serve as the basis for a one-semester course on the cohomology of sheaves and its relation to real and complex manifolds.” (Rui Miguel Saramago, zbMATH 1361.55001, 2017)

Authors and Affiliations

  • Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Torsten Wedhorn

About the author

Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany

Bibliographic Information

Buy it now

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access