Assembly maps, \(K\)-theory, and hyperbolic groups (Q1207507)

The author begins by constructing generalized assembly maps in topological, algebraic and Hermitian \(K\)-theory. He then shows that the topological version is injective after tensoring with the complex numbers, provided that the group involved satisfies suitable conditions. In particular, the result holds if the group is finitely generated and word-hyperbolic. There is an analogous result in algebraic \(K\)-theory. From the topological result it follows that the equivariant Novikov conjecture holds for the groups concerned.