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Infinite loop structures on the algebraic K-theory of spaces

Published online by Cambridge University Press:  24 October 2008

Richard J. Steiner
Richard J. Steiner
Affiliation:
University of Glasgow
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Extract

Let X be a topological space with base-point. The algebraic K-theory AX of X is a space invented by Waldhausen in (15) for use in geometric topology. It can be defined in two ways, which I shall call geometric and ring-theoretic; Steinberger ((12)) has shown them to be equivalent.

The geometric method ((15), corollary to lemma 2·1) gives AX as the group-completion of the geometric realization of a permutative category. It follows from the machinery of May ((4), 4) or Segal (11) that AX is an infinite loop space in a well-defined way ((6)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 85 - 111
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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