Bounded Cohomology Characterizes Hyperbolic Groups

Bounded Cohomology and Combings of Groups

We adopt the notion of combability of groups defined in [Ghys2]. An example is given of a combable group which is not residually finite. Two of the eight 3-dimensional geometries, e Sl2(R) and H ×R, are quasiisometric. Three dimensional geometries are classified up to quasiisometry. Seifert fibred manifolds over hyperbolic orbifolds have bicombable fundamental groups. Every combable group satis...

Bounded Cohomology, Cross Ratios and Cocycles

We use cross ratios to describe second real continuous bounded cohomology for locally compact σ-compact topological groups. We also investigate the second continuous bounded cohomology group of a closed subgroup of the isometry group Iso(X) of a proper hyperbolic geodesic metric space X and derive some rigidity results for Iso(X)-valued cocycles.

Central Extensions of Word Hyperbolic Groups

Thurston has claimed (unpublished) that central extensions of word hyperbolic groups by finitely generated abelian groups are automatic. We show that they are in fact biautomatic. Further, we show that every 2-dimensional cohomology class on a word hyperbolic group can be represented by a bounded 2-cocycle. This lends weight to the claim of Gromov that for a word hyperbolic group, the cohomolog...

The second bounded cohomology of word-hyperbolic groups

B-Bounded Cohomology and Applications

A discrete group with word-length (G,L) is B -isocohomological for a bounding classes B if the comparison map from B -bounded cohomology to ordinary cohomology (with coefficients in C) is an isomorphism; it is strongly B isocohomological if the same is true with arbitrary coefficients. In this paper we establish some basic conditions guaranteeing strong B -isocohomologicality. In particular, we...