Manifolds, Sheaves, and Cohomology

  • Torsten Wedhorn

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Torsten Wedhorn
    Pages 1-20
  3. Torsten Wedhorn
    Pages 21-40
  4. Torsten Wedhorn
    Pages 41-68
  5. Torsten Wedhorn
    Pages 69-90
  6. Torsten Wedhorn
    Pages 91-121
  7. Torsten Wedhorn
    Pages 123-137
  8. Torsten Wedhorn
    Pages 139-151
  9. Torsten Wedhorn
    Pages 153-192
  10. Torsten Wedhorn
    Pages 193-204
  11. Torsten Wedhorn
    Pages 205-232
  12. Torsten Wedhorn
    Pages 233-244
  13. Torsten Wedhorn
    Pages 245-269
  14. Torsten Wedhorn
    Pages 271-290
  15. Torsten Wedhorn
    Pages 291-315
  16. Torsten Wedhorn
    Pages 317-330
  17. Torsten Wedhorn
    Pages 331-340
  18. Back Matter
    Pages 341-354

About this book

Introduction

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.

Content
Topological Preliminaries - Algebraic Topological Preliminaries - Sheaves - Manifolds - Local Theory of Manifolds - Lie Groups - Torsors and Non-abelian Cech Cohomology - Bundles - Soft Sheaves - Cohomology of  Complexes of Sheaves - Cohomology of Sheaves of Locally Constant Functions - Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis

Readership
Graduate Students in Mathematics / Master of Science in Mathematics 

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

Keywords

Bundles Cohomology Lie Groups Manifolds Sheaves

Authors and affiliations

  • Torsten Wedhorn
    • 1
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-658-10633-1
  • Copyright Information Springer Fachmedien Wiesbaden 2016
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-658-10632-4
  • Online ISBN 978-3-658-10633-1
  • About this book