AMCA: Residually finite hyperbolic groups and dynamics of polynomial maps over $Z

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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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Residually finite hyperbolic groups and dynamics of polynomial maps over Z_p
by
Mark Sapir
Vanderbilt

We study polynomial maps f:Z_pⁿ --> Z_pⁿ and their dynamics properties (here Z_p is the ring of p-adic integers). A typical result: if dist(f(a), a) < 1/p² and J_f(a) =/= 0 then a is a recurrent point for f. Using these results we prove that certain maping tori over free groups are residually finite. We shall also mention open problems and conjectures which could lead to construction of a non-residually finite hyperbolic group.

Date received: April 15, 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 Mathematical Conference Abstracts. Document # cabb-18.