Coverart for item
The Resource Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)

Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)

Label
Introductory Lectures on Equivariant Cohomology : (AMS-204)
Title
Introductory Lectures on Equivariant Cohomology
Title remainder
(AMS-204)
Statement of responsibility
Loring W. Tu
Creator
Subject
Language
  • eng
  • eng
Summary
This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics.Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study
Is part of
Cataloging source
DE-B1597
http://library.link/vocab/creatorName
Tu, Loring W
Government publication
other
Language note
In English
Nature of contents
dictionaries
Series statement
Annals of Mathematics Studies
Series volume
204
http://library.link/vocab/subjectName
  • Cohomology operations
  • Homology theory
Target audience
specialized
Label
Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)
Instantiates
Publication
Contents
  • Part IV. Borel Localization
  • Part V. The Equivariant Localization Formula
  • Appendices
  • Hints and Solutions to Selected End-of-Section Problems
  • List of Notations
  • Bibliography
  • Index
  • Frontmatter
  • Contents
  • List of Figures
  • Preface
  • Acknowledgments
  • Part I. Equivariant Cohomology in the Continuous Category
  • Part II. Differential Geometry of a Principal Bundle
  • Part III. The Cartan Model
Control code
ssj0002346969
Dimensions
unknown
Extent
1 online resource (200 p.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9780691197487
Lccn
2019048303
Other control number
10.1515/9780691197487
Other physical details
37 b/w illus
Specific material designation
remote
System control number
(WaSeSS)ssj0002346969
System details
Mode of access: Internet via World Wide Web
Label
Introductory Lectures on Equivariant Cohomology : (AMS-204), Loring W. Tu, (electronic resource)
Publication
Contents
  • Part IV. Borel Localization
  • Part V. The Equivariant Localization Formula
  • Appendices
  • Hints and Solutions to Selected End-of-Section Problems
  • List of Notations
  • Bibliography
  • Index
  • Frontmatter
  • Contents
  • List of Figures
  • Preface
  • Acknowledgments
  • Part I. Equivariant Cohomology in the Continuous Category
  • Part II. Differential Geometry of a Principal Bundle
  • Part III. The Cartan Model
Control code
ssj0002346969
Dimensions
unknown
Extent
1 online resource (200 p.)
Form of item
online
Governing access note
Access restricted to subscribing institutions
Isbn
9780691197487
Lccn
2019048303
Other control number
10.1515/9780691197487
Other physical details
37 b/w illus
Specific material designation
remote
System control number
(WaSeSS)ssj0002346969
System details
Mode of access: Internet via World Wide Web

Library Locations

    • Bowdoin College LibraryBorrow it
      3000 College Station, Brunswick, ME, 04011-8421, US
      43.907093 -69.963997