The Homology of Iterated Loop Spaces
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533 Frederick R.Cohen ThomasJ. Lada J. Peter May
The Homology of Iterated Loop Spaces
Springer-Verlag Berlin. Heidelberg. New York 1976
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
533 Frederick R.Cohen ThomasJ. Lada J. Peter May
The Homology of Iterated Loop Spaces
Springer-Verlag Berlin. Heidelberg. New York 1976
Authors
Frederick R. C o h e n Department of Mathematics Northern Illinois University DeKalb, Illinois 6 0 1 1 5 / U S A
Thomas J. Lada Department of Mathematics North Carolina State University Raleigh, North Carolina 2 7 6 0 7 / U S A J. Peter May Department of Mathematics University of C h i c a g o Chicago, Illinois 6 0 6 3 7 / U S A
Library of Congress Cataloging in Publication Data
Cohen, Frederick Ronald, 1946The homology of iterated loop spaces. (Lecture notes in mathematics ; 533) Bibliography: p. Includes index. i. Loop spaces. 2. ClasSifying spaces. 3. Homology theory. I. Lada~ Thomas Joseph, 1946joint author. II. May, J. Peter, joint author. II. May, J. Peter~ joint author. III. Title. IV. Series : Lecture notes in mathematics (Berlin) ; 533. QA3.L28 vol. 5033 [QA612.76] 510'.8s [514'.2]
AMS Subject Classifications (1970): 18F25, 18H10, 55D35, 55D40, 55F40, 5 5 G 9 9
ISBN 3-540-07984-X Springer-Verlag Berlin 9 Heidelberg 9 New York ISBN 0-387-07984-X Springer-Verlag New York 9 Heidelberg 9 Berlin
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Preface
This v o l u m e is a collection of five papers (to be referred to as I-V).
T h e first four together give a thorough treatment of h o m o l o g y
operations and of their application to the calculation of, and analysis of internal structure in, the homologies of various spaces of interest. The last studies an up to h o m o t o p y notion of an algebra over a m o n a d and the role of this notion in the theory of itex,ated loop spaces.
I have
established the algebraic preliminaries necessary to the first four papers and the geometric preliminariesnecessary for all of the papers in the following references, which shall be referred to by the specified letters throughout the volume. [A].
A general algebraic approach to Steenrod operations.
Springer
Lecture Notes in Mathematics Vol. 168, i970, 153-231. [G].
The G e o m e t r y of Iterated L o o p Spaces. Springer Lecture Notes in M a t h e m a t i c s Vol. 27i, i972.
[G']. E
oo
spaces, group completions, and permutative categories.
L o n d o n Math. Soc. Lecture Note Series Vol. II, 1974, 61-93. In addition,
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