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Cohomology Theory of Topological Transformation Groups

  • Book
  • © 1975

Overview

Authors:
  1. Wu Yi Hsiang

    1. Department of Mathematics, University of California, Berkeley, USA

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 85)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Generalities on Compact Lie Groups and G-Spaces

    • Wu Yi Hsiang
    Pages 1-16

  3. Structural and Classification Theory of Compact Lie Groups and Their Representations

    • Wu Yi Hsiang
    Pages 17-32

  4. An Equivariant Cohomology Theory Related to Fibre Bundle Theory

    • Wu Yi Hsiang
    Pages 33-42

  5. The Orbit Structure of a G-Space X and the Ideal Theoretical Invariants of H * G (X)

    • Wu Yi Hsiang
    Pages 43-69

  6. The Splitting Principle and the Geometric Weight System of Topological Transformation Groups on Acyclic Cohomology Manifolds or Cohomology Spheres

    • Wu Yi Hsiang
    Pages 70-104

  7. The Splitting Theorems and the Geometric Weight System of Topological Transformation Groups on Cohomology Projective Spaces

    • Wu Yi Hsiang
    Pages 105-128

  8. Transformation Groups on Compact Homogeneous Spaces

    • Wu Yi Hsiang
    Pages 129-159

  9. Back Matter

    Pages 160-166
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Keywords

About this book

Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L. E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or non-existence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P. A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups.

Authors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Wu Yi Hsiang

Bibliographic Information

  • Book Title: Cohomology Theory of Topological Transformation Groups

  • Authors: Wu Yi Hsiang

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-66052-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1975

  • Softcover ISBN: 978-3-642-66054-2Published: 16 December 2011

  • eBook ISBN: 978-3-642-66052-8Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 166

  • Topics: Topology

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