On transfer in bounded cohomology

We define a transfer map in the setting of bounded cohomology with certain metric G-module coefficients. As an application, we extend a theorem of Chatterji, Mislin, Pittet and Saloff-Coste on the comparison map from Borel-bounded to Borel cohomology, to cover the case of Lie groups with finitely many connected components.Comment: 8 page

Hattori-Stallings trace and Euler characteristics for groups

We discuss properties of the complete Euler characteristic of a group G of type FP over the complex numbers and we relate it to the L2-Euler characteristic of the centralizers of the elements of G.Comment: To appear in: London Math. Society Lecture Note Series, Vol 358, 200

The geometric realization of Wall obstructions by nilpotent and simple spaces

Let π denote a finite group. It is well known that every element of the projective class group K0 ℤπ may be realized as Wall obstruction of a finitely dominated complex with fundamental group π (cf. (13)). We will study two subgroups N0ℤπ and Nℤπ of K0ℤπ, which are closely related to the Wall obstruction of nilpotent spaces. If the group π is nilpotent and if S denotes the set of elements x K0ℤπ which occur as Wall obstructions of nilpotent spaces, then It turns out that in many instances one has N0,ℤπ = Nℤπ (cf. Section 3) and one obtains hence new information on S. The main theorem (2·4) provides a systematic way of constructing finitely dominated nilpotent (or even simple) spaces with non-vanishing Wall obstruction

Bounded characteristic classes and flat bundles

Let G be a connected Lie group, G^d the underlying discrete group, and BG, BG^d their classifying spaces. Let R denote the radical of G. We show that all classes in the image of the canonical map in cohomology H^*(BG,R)->H^*(BG^d,R) are bounded if and only if the derived group [R,R] is simply connected. We also give equivalent conditions in terms of stable commutator length and distortion.Comment: 12 pages, no figur