Homological Characterization of Distortion and Hyperbolicity
by
Steve Gersten
University of Utah

The first of the two talks will give a homological characterization for when a finitely generated subgroup of a finitely generated group is undistorted for their respective word metrics in terms of their l₁-zero dimensional homology groups. The second talk will give a homological characterization of hyperbolic groups, as those finitely presented groups for which every summable 1-cycle is a summable boundary and for which every summable 2-cycle can be approximated by 2-cycles of compact support. Both results depend on an approximation theorem: every summable real valued 1-cycle on a graph can be approximated by 1-cycles of compact support.

Date received: February 27, 1998

Copyright © 1998 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 # cabg-03.