Infinite loop structures on the algebraicK-theory of spaces

Abstract

LetXbe a topological space with base-point. Thealgebraic K-theory AXofXis a space invented by Waldhausen in (15) for use in geometric topology. It can be defined in two ways, which I shall callgeometricandring-theoretic; Steinberger ((12)) has shown them to be equivalent.The geometric method ((15), corollary to lemma 2·1) givesAXas the group-completion of the geometric realization of a permutative category. It follows from the machinery of May ((4), 4) or Segal (11) thatAXis an infinite loop space in a well-defined way ((6)).