The cyclotomic trace and the K-theoretic analogue of Novikov's conjecture

AUTOR(ES)

Bökstedt, M.

RESUMO

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.

Documentos Relacionados

• Excision in algebraic K-theory and Karoubi's conjecture.
• The homogeneity conjecture
• FAKE TORI, THE ANNULUS CONJECTURE, AND THE CONJECTURES OF KIRBY*
• The strong Nagata conjecture
• A conjecture of Procesi and the straightening algorithm of Rota.