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International Conference on Non-Positive Curvature in Group Theory, Topology, and Geometry
May 28-31, 1998
Vanderbilt University
Nashville, TN, USA

Organizers
B. Hughes, M. Mihalik, E. Prassidis, J. Ratcliffe, K. Ruane, M. Sapir, E. Schechter

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Detour functions and quasi-isometries
by
Natasa Macura
University of Utah

We show that the mapping tori of two automorphisms of finitely generated free groups that grow polynomially with different degree cannot be quasi-isometric. In order to do that we introduce detour functions, real functions defined on a proper metric space which are invariant under quasi-isometries. We prove that the mapping torus of an automorphism of a free group Fn which grows polynomially with a degree d >= 1 has a detour function that is a polynomial of degree d+1.

Date received: April 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 # cabb-39.