Title: Rational
injectivity of the Farrell-Jones assembly map for
algebraic K-theory
Abstract: A
consequence of the Farrell-Jones Conjecture says that the
assembly map from the equivariant homology theory
$H_n(\underline{E};K)$ associated to algebraic K-theory and the space
of proper $G$-actions to the algebraic $K$-group $K_n({\mathbb
Z}G)$ is rationally bijective. We prove this for groups satisfying some
homological finiteness conditions and under a certain number theoretic
assumption which is satisfied in certain cases. This result generalizes
substantially the proof of Boekstedt-Hsiang-Madsen of the K-theoretic
Novikov Conjecture. This is joint work with Holger reich, John Rognes
and Marco Varisco.