Introductory lectures on equivariant cohomology : (with appendices by Loring W. Tu and Alberto Arabia) /

"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 in...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Tu, Loring W. (Author)
Other Authors: Arabia, Alberto (Contributor)
Format: Electronic eBook
Language:Inglés
Published: Princeton : Princeton University Press, 2020.
Series:Annals of mathematics studies ; no. 204.
Subjects:
Homology theory.
Homologie.
MATHEMATICS > Geometry > Algebraic.
Online Access:Texto completo
Table of Contents:
  • Homotopy groups and CW complexes
  • Principal bundles
  • Homotopy quotients and equivariant cohomology
  • Universal bundles and classifying spaces
  • Spectral sequences
  • Equivariant cohomology of S² under rotation
  • A universal bundle for a compact lie group
  • General properties of equivariant cohomology
  • The lie derivative and interior multiplication
  • Fundamental vector fields
  • Basic forms
  • Integration on a compact connected lie group
  • Vector-valued forms
  • The Maurer-Cartan form
  • Connections on a principal bundle
  • Curvature on a principal bundle
  • Differential graded algebras
  • The Weil algebra and the weil model
  • Circle actions
  • The cartan model in general
  • Outline of a proof of the equivariant de Rham theorem
  • Localization in algebra
  • Free and locally free actions
  • The topology of a group action
  • Borel localization for a circle action
  • A crash course in representation theory
  • Integration of equivariant forms
  • Rationale for a localization formula
  • Localization formulas
  • Proof of the localization formula for a circle action
  • Some applications.

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