Geometric Methods in Degree Theory for Equivariant Maps

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.

Contenu

Fundamental domains and extension of equivariant maps.- Degree theory for equivariant maps of finite-dimensional manifolds: Topological actions.- Degree theory for equivariant maps of finite-dimensional manifolds: Smooth actions.- A winding number of equivariant vector fields in infinite dimensional banach spaces.- Some applications.