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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.
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