Frobenius Induction for Higher Whitehead Groups

Abstract

The theory of induced representations has served as a powerful tool in the computations of algebraicK-theory andL-theory ([2], [7], [4, 5], [9], [10, 11, 12, 13], [14], [17], [18]). In this paper we show how to apply this theory to obtain induction theorems for the higher Whitehead groups of Waldhausen. The same technique applies to the analogs of Whitehead groups in unitaryK-theory and inL-theory.For any ringAwith unit, letK(A) be the spectrum of the algebraicK-theory ofA([8, p. 343]). Given a discrete group Γ and a subringRof the rational numbers, Loday defines a map of spectra:*where (BΓ) is the classifying space of Γ union with a disjoint base point andRΓ is the group-ring of Γ overR.