Bounded Cocycles and Combings of Groups

We adopt the notion of combability of groups defined in 12. An example is given of a (bi-)combable group which is not residually finite. Two of the eight 3-dimensional geometries, Formula: see text and ℍ 2 ×ℝ, are quasiisometric. Seifert fibred manifolds over hyperbolic orbifolds have bicombable fundamental groups. Every combable group satisfies an exponential isoperimetric inequality.