Author: Kiang Tsai-han
Language: English
Published on: 1989-01
Hardcover
The Theory of Fixed Point Classes (also known as Nielsen fixed point theory)examines the fixed points of an arbitrary mapping of any connected finite polyhedron into itself. Its main problem is to determine a lower bound of the geometric countings (i.e.the actual numbers) of fixed poinits of all mappings homotopic to the given mapping. The existence problem of fixed points is evidently a particular case.
Language: English
Published on: 1989-01
Hardcover
The Theory of Fixed Point Classes (also known as Nielsen fixed point theory)examines the fixed points of an arbitrary mapping of any connected finite polyhedron into itself. Its main problem is to determine a lower bound of the geometric countings (i.e.the actual numbers) of fixed poinits of all mappings homotopic to the given mapping. The existence problem of fixed points is evidently a particular case.
The present book is an English translation of the revised second Chinese edition. It is a fundamental representation of the important theory, presented in a more elementary and geometric way than the existing literature.
CONTENTS
CHAPTER I. The General Problem. A Particular Case. A Few Historical Remarks
Chapter II The Nielsen Number
Chapter III Evaluation of the Nielsen Number
Chapter IV Nielsen Number and the Least Number of Fixed Points
Chapter V The Number N(f; H) and the Root Classes
Appendix A. Homotopy and Fundamental Group
Appendix B. Covering Spaces
Appendix C. Appoximation Theorems
Bibliography
Epilogue
List of symbols
Index
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