2 Wolfgang Lück and Holger

Equivariant covers for hyperbolic groups

Recall that a cover U is of dimension N if every x 2 X is contained in no more then N C 1 members of U . The asymptotic dimension of a finitely generated group is its asymptotic dimension as a metric space with respect to any word metric. An important result of Yu [19] asserts that the Novikov conjecture holds for groups of finite asymptotic dimension. This can be viewed as an injectivity resul...

Detecting K-theory by Cyclic Homology

We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology.

Novikov-Shubin invariants for arbitrary group actions and their positivity

We extend the notion of Novikov-Shubin invariant for free Γ-CW complexes of finite type to spaces with arbitrary Γ-actions and prove some statements about their positivity. In particular we apply this to classifying spaces of discrete groups.

Equivariant homology theory and assembly maps by Wolfgang Lück ( Münster ) July 2006

Geodesic flow for CAT.0/–groups

In Bartels–Lück [1] we introduced the concept of transfer reducible groups with respect to a family of subgroups. This definition is somewhat technical and recalled as Definition 0.4 below. We showed that groups that are transfer reducible over the family of virtually cyclic subgroups satisfy the Farrell–Jones Conjecture with coefficients in an additive category. For further explanations about ...