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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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The Large Scale Geometry of PSL2 (Z[1/p])
by
Jennifer Taback
University of Chicago

I will describe the geometry of the group PSL2(Z[1/p]) and construct a space on which it acts properly discontinuously and cocompactly by isometries. The solvable Baumslag-Solitar groups BS(1, n) also play a role in the geometry of this space. I will briefly discuss my results on the quasi-isometric rigidity of PSL2(Z[1/p]) :

PSL2(Z[1/p]) is uniquely determined up to quasi-isometry among all finitely generated groups.

PSL2(Z[1/p]) and PSL2(Z[1/q]) are not quasi-isometric unless p=q.

The quasi-isometry group of PSL2(Z[1/p]) is isomorphic to its commensurator group PGL2(Q).

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-17.