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Cohomology Theory of Topological Transformation Groups by W Y Hsiang
Cohomology Theory of Topological Transformation Groups by W Y Hsiang
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Cohomology Theory of Topological Transformation Groups

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Description

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.
Release date Australia
December 16th, 2011
Author
Audience
  • Professional & Vocational
Edition
Softcover reprint of the original 1st ed. 1975
Illustrations
X, 166 p.
Pages
166
Dimensions
170x244x9
ISBN-13
9783642660542
Product ID
20771837

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