Bounded cohomology for surface groups

Bounded Cohomology Characterizes Hyperbolic Groups

A finitely presentable group G is hyperbolic if and only if the map H2 b (G, V ) → H2(G, V ) is surjective for any bounded G-module. The ‘only if’ direction is known and here we prove the ‘if’ direction. We also consider several ways to define a linear homological isoperimetric inequality.

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...

Polynomially bounded cohomology and discrete groups

We establish the homological foundations for studying polynomially bounded group cohomology, and show that the natural map from PH∗(G;Q) to H∗(G;Q) is an isomorphism for a certain class of groups. © 2004 Elsevier B.V. All rights reserved. MSC: 18G10; 18G40; 13D99; 16E30; 20J05; 20F05; 20F65

Bounded Cohomology and Non-uniform Perfection of Mapping Class Groups

Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive genus. This estimate is then used to deduce that mapping class groups are not uniformly perfect, and that the map from their second bounded cohomology to ordi...

The second bounded cohomology of word-hyperbolic groups