Straightening and bounded cohomology of hyperbolic groups
by
Igor Mineyev
Max-Planck-Institut für Mathematik

It was claimed by M. Gromov in "Hyperbolic groups" that the cohomology of hyperbolic groups is bounded (for real coefficients in the dimensions 2 and higher). We prove, more generally, that, for any hyperbolic group G, the map

Hkb(G, V) --> Hk(G, V)

(induced by inclusion) is surjective, where k >= 2 and V is either any normed vector space over the rationals or any finitely generated abelian group.

The idea of the proof is different from the one suggested in the book. We introduce a homological version of straightening for hyperbolic groups, which is analogous to the straightening in hyperbolic manifolds.

The paper is available at http://www.math.utah.edu/~mineyev/math/

Date received: January 11, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-06.