文档介绍：Lecture Notes in Mathematics
A collection of informal reports and seminars
Edited by A. Dold, Heidelberg and B. Eckmann, ZUrich
28
P. E. Conner. E, E. Floyd
University of Virginia, Charlottesville
The Relation
of Cobordism to K-Theories
1966 m I
Springer-Verlag. Berlin-Heidelberg-New York
All rights, especially that of translation 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. © by Springer-Verlag Berlin • Heidelberg 1966.
Library of Congress Catalog Card Number 66-30143. Printed in Germany. Title No. 7348.
INTRODUCTION
These lectures treat certain topics relating K-theory and cobordism.
Since new connections are in the process of being discovered by various
workers, we make no attempt to be definitive but simply cover a few of
our favorite topics. If there is any unified theme it is that we treat
various generalizations of the Todd genus.
In Chapter I we treat the Thom isomorphism in K-theory. The
families U, SU, Sp of unitary, special unitary, symplectic groups
generate spectra MU, MSU, HSp of Thom spaces. In the fashion of
G. W. Whitehead [2B], each spectrum generates a generalized cohomology
theory and a generalized homology theory. The cohomology theories are
denoted by t~*~ (.),~ * (.), ~ . (.) and are called cobordism theories;
U SU Sp ~U . _ SU . Sp(.) .
the homology theories are denoted by~.[ ),/~. ( ),~ and are
called bordism theories. The coefficient groups are, taking one case
as an example, given by~ Un =/~n (point),~U =~U (point) and are
U n n
related by~ Un = .1~ -n U . M°re°ver~U is Just the bordism group of all
n
bordism classes [Mn] of closed weakly plex manifolds M n,
similarly for~ SU and~ Sp. On the other hand there are the
n n
Grothendieck-Atlyah-Hirzebruch periodic cohomolog