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.
General
Imprint: |
Springer-Verlag
|
Country of origin: |
Germany |
Series: |
Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 85 |
Release date: |
December 2011 |
First published: |
1975 |
Authors: |
W.Y. Hsiang
|
Dimensions: |
244 x 170 x 9mm (L x W x T) |
Format: |
Paperback
|
Pages: |
166 |
Edition: |
Softcover reprint of the original 1st ed. 1975 |
ISBN-13: |
978-3-642-66054-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
General
|
LSN: |
3-642-66054-1 |
Barcode: |
9783642660542 |
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!