Equivariant Surgery Theories and Their Periodicity Properties

Karl Heinz Dovermann, Reinhard Schultz (auth.)3540530428, 9783540530428, 0387530428

The theory of surgery on manifolds has been generalized to categories of manifolds with group actions in several different ways. This book discusses some basic properties that such theories have in common. Special emphasis is placed on analogs of the fourfold periodicity theorems in ordinary surgery and the roles of standard general position hypotheses on the strata of manifolds with group actions. The contents of the book presuppose some familiarity with the basic ideas of surgery theory and transformation groups, but no previous knowledge of equivariant surgery is assumed. The book is designed to serve either as an introduction to equivariant surgery theory for advanced graduate students and researchers in related areas, or as an account of the authors’ previously unpublished work on periodicity for specialists in surgery theory or transformation groups.

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Table of contents :
Summary: Background material and basic results….Pages 1-8
Introduction to equivariant surgery….Pages 9-36
Relations between equivariant surgery theories….Pages 37-79
Periodicity theorems in equivariant surgery….Pages 80-114
Twisted product formulas for surgery with coefficients….Pages 115-140
Products and periodicity for surgery up to pseudoequivalence….Pages 141-191