Let X → A(X) denote the algebraic K-theory of spaces functor. In the first paper of this series, we showed A(X × S1) 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) script capital L sign.-construction. The main result is proved using this alternative discription. © 2002 Elsevier Science B.V. All rights reserved.
Huttemann, T., Klein, J. R., Vogell, W., Waldhausen, F., & Williams, B. (2002). The “fundamental theorem” for the algebraic K-theory of spaces: II - The canonical involution. Journal of Pure and Applied Algebra, 167(1), 53–82. https://doi.org/10.1016/S0022-4049(01)00067-6