文档介绍：Lecture Notes in Mathematics
A collection of informal reports and seminars
Edited by A. Dold, Heidelberg and B. Eckmann, Z0rich
34
Glen E. Bredon
University of California, Berkeley
Equivariant
Cohomology Theories
1967
.. y
Springer-Verlag. Berlin. Heidelberg-New York
ALl rights, especially that of tran~ation into foreign languages, reserved. It is also forbidden to reproduce this book, either
whole or in part, by photomechanical means (photostat, microfilm and/or microcard)or by other procedure without
written permission from Springer Verlag. O by Sprtnger-Verlag Berlin Heidelberg 1967~
-Library of Congress Catalog Card Number 67 - 25284 Printed in Germany. Title No. 7354.
Preface
These notes constitute the lecture notes to a series of
lectures which the author gave at Berkeley in the spring of
1966.
Our central objective is to provide machinery for the
study of the set [[XIY]] of equivariant homotopy classes of
equivariant maps from the G-space X to the G-space Y (with base
points fixed by G). (For various reasons we restrict our atten-
tion to the case in which G is a finite group.) An important
tool for this study is equivariant cohomology theory. It is
immediately seen, however, that the classical equivariant
cohomology theory is quite inadequate for the task.
Our first object then is to develop an "equivariant
classical cohomology theory" (as opposed to "classical equi-
variant cohomology theory") which is putable and
which, for example, allows the development of an equivariant
obstruction theory. This is done in Chapter I and the obstruction
theory is considered in Chapter If. Our cohomology theory
includes the classical theory as a special case.
An approximation to [[X~Y]] is the stable object
lim[[snx~ S n Y]] which forms a group. If Y is a sphere, with a
given G-action, this leads to the stable equivariant cohomotopy
groups of a G-space X. These form an "equivariant general