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Homology Operations Revisited

Published online by Cambridge University Press:  20 November 2018

Z. Fiedorowicz  and
J. P. May
Z. Fiedorowicz
Affiliation:
Ohio State University, Columbus, Ohio
J. P. May
Affiliation:
The University of Chicago, Chicago, Illinois
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There are two principal kinds of input data for infinite loop space theory, namely E∞ spaces à la Boardman-Vogt [3] and May [7] and Γ-spaces à la Segal [14]. May and Thomason [13] introduced a common generalization and used it to prove the equivalence of the output obtained from these two kinds of input.

This suggests that any invariants of one kind of input should have analogs for the other. Homology operations are among the most basic invariants of E∞ spaces, and we here establish the analogous invariants for Γ-spaces. The definition is transparently obvious from the point of view of the common generalization but is at first sight rather surprising and unnatural from the point of view of Γ-spaces alone. Probably for this reason, there is no hint of the possibility of a direct definition of homology operations for Γ-spaces in the literature.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 3 , 01 June 1982 , pp. 700 - 717
Copyright
Copyright © Canadian Mathematical Society 1982

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