Geometric Methods in Degree Theory for Equivariant Maps

1. Front Matter

   Pages I-VI

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2. Introduction

   • Alexander Kushkuley, Zalman Balanov

   Pages 1-12

3. Fundamental domains and extension of equivariant maps

   • Alexander Kushkuley, Zalman Balanov

   Pages 13-30

4. Degree theory for equivariant maps of finite-dimensional manifolds: Topological actions

   • Alexander Kushkuley, Zalman Balanov

   Pages 31-42

5. Degree theory for equivariant maps of finite-dimensional manifolds: Smooth actions

   • Alexander Kushkuley, Zalman Balanov

   Pages 43-73

6. A winding number of equivariant vector fields in infinite dimensional banach spaces

   • Alexander Kushkuley, Zalman Balanov

   Pages 74-85

7. Some applications

   • Alexander Kushkuley, Zalman Balanov

   Pages 86-125

8. Back Matter

   Pages 126-136

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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.
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.

• Equivariant topology
• Homotopy
• Winding number
• manifold
• nonlinear analysis

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