Equivariant Surgery Theories and Their Periodicity Properties
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 four
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Karl Heinz Dovermann Reinhard Schultz
Equivariant SurgeryTheories and Their Periodicity Properties
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Authors
Karl Heinz Dovermann Department of Mathematics, University of Hawaii Honolulu, Hawaii 96822, USA Reinhard Schultz Department of Mathematics, Purdue University West Lafayette, Indiana 47907, USA
Mathematics Subject Classification (1980): Primary: 57R67, 57S17 Secondary: 18F25 ISBN 3-540-53042-8 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-53042-8 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1990 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper
PREFACE
This book began as a pair of papers covering the authors' work on periodicity in equivariant surgery from late 1982 to mid 1984. Since our results apply to many different versions of equivariant surgery theory, it seemed desirable to provide a unified approach to these results based upon formal properties that hold in all the standard theories. Although workers in the area have been aware of these common properties for some time, relatively little has been written on the subject. Furthermore, it is not always obvious how the settings for different approaches to equivariant surgery are related to each other, and this can make it difficult to extract the basic properties and interrelationships of equivariant surgery theories from the literature. For these and other reasons we eventually decided to include a survey of equivariant surgery theories that would present their basic formal properties. Shortly after we began revising our papers to include such a survey, Wolfgang Luck and Ib Madsen began work on a more abstractand in many respects more generalapproach to equivariant surgery. It became increasingly clear that we should include their methods and results in our book, not only for the sake of completeness but also because their work leads to improvements in the exposition, simplifications of some proofs, and significant extensions of our main results and applications. The inclusion of Luck and Madsen's work and its effects on our own work are two excuses for the four year delay in revising our original two papers. Our initial work on equivariant periodicity appears in Chapters III through V. The first two chapters summarize the main versions of equivariant surgery and the basic formal properties o
