The 'fundamental theorem' for the algebraic K-theory of spaces: II - the canonical involution

摘要

Let X --> A(X) denote the algebraic K-theory of spaces functor. In the first paper of this series, we showed A(X x S-1) decomposes into a product of a copy of A(X), a delooped copy of A(X) and two homeomorphic nil terms. The primary goal of this paper is to determine how the "canonical involution" acts on this splitting. A consequence of the main result is that the involution acts so as to transpose the nil terms. From a technical point of view, however, our purpose will be to give another description of the involution on A(X) which arises as a (suitably modified) P.-construction. The main result is proved using this alternative discription. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 9]