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G^3 = Geometric Group Theory on the Gulf Coast
March 15-17, 2002
The University of New Orleans and the University of South Alabama
New Orleans, LA, USA

Organizers
Stephen Brick, Craig Jensen, Igor Mineyev

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The geometry of Schreier graphs for subgroups of hyperbolic groups
by
Ilya Kapovich
University of Illinois at Urbana-Champaign

We show that if H is a quasiconvex subgroup of a hyperbolic group G then the Schreier coset graph X for G with respect to H is Gromov-hyperbolic and has positive Cheeger constant (i.e. is non-amenable) provided G is non-elementary and H has infinite index in G.

This implies a number of corollaries regarding the Martin boundary of the simple random walk on X and the co-growth of H in G.

Paper reference: arXiv:math.GR/0201076

Date received: March 4, 2002

Copyright © 2002 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 # caja-03.