The cyclotomic trace and the K-theoretic analogue of Novikovs conjecture

摘要

A trace construction, the cyclotomic trace, is given. It associates to algebraic K-theory of a group ring, or better to Waldhausen's A-theory, equivariant stable homotopy classes of the free-loop space of its classifying space. The cyclotomic trace detects the Borel classes in algebraic K-theory of the integers. It is used to prove, for a wide class of groups, that the K-theory assembly map is rationally injective. This is the K-theoretic analogue of Novikov's conjecture.