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The Group of Units in K-Theory Modulo an Odd Prime

Published online by Cambridge University Press:  20 November 2018

R. J. Steiner
R. J. Steiner*
Affiliation:
University of Western Ontario, London, Ontario
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1. Introduction. There are several multiplicative cohomology theories for which the group of units in the zeroth term is the zeroth term of another cohomology theory. Examples, due to Segal, May and others, are given by ordinary cohomology with rather general graded coefficients, real and complex K-theory with integral coefficients, and various bordism theories, also with integral coefficients [8, 7, 2, 5, IV]. The object of this paper is to show that complex K-theory modulo an odd prime p provides a counter-example.

To state the theorem precisely we recall the result of Araki and Toda that there is a unique anticommutative associative admissible multiplication in K*( ;Z/p) for p an odd prime [3, 3, 7, 10]; admissible is defined in [3] and means essentially that the reduction homomorphism K*( ) → K*( ; Z/p) preserves products.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 5 , 01 October 1979 , pp. 915 - 928
Copyright
Copyright © Canadian Mathematical Society 1979

References

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