Geometric Methods in Degree Theory for Equivariant Maps

Alexander Kushkuley, Zalman Balanov (auth.)3540615296, 9783540615293

The book introduces conceptually simple geometric ideas based on the existence of fundamental domains for metric G- spaces. A list of the problems discussed includes Borsuk-Ulam type theorems for degrees of equivariant maps in finite and infinite dimensional cases, extensions of equivariant maps and equivariant homotopy classification, genus and G-category, elliptic boundary value problem, equivalence of p-group representations.
The new results and geometric clarification of several known theorems presented here will make it interesting and useful for specialists in equivariant topology and its applications to non-linear analysis and representation theory.

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Table of contents :
Introduction….Pages 1-12
Fundamental domains and extension of equivariant maps….Pages 13-30
Degree theory for equivariant maps of finite-dimensional manifolds: Topological actions….Pages 31-42
Degree theory for equivariant maps of finite-dimensional manifolds: Smooth actions….Pages 43-73
A winding number of equivariant vector fields in infinite dimensional banach spaces….Pages 74-85
Some applications….Pages 86-125