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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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Symmetries of Outer Space
by
Karen Vogtmann
Cornell University
Coauthors: Martin Bridson

The group Out(Fn) of outer automorphisms of a finitely generated free group acts on a certain contractible simplicial complex Kn, called the spine of outer space. We show that in fact Out(Fn) is the full group of simplicial automorphisms of Kn. This is analogous to Royden's theorem that the mapping class group is the full group of isometries of Teichmüller space, or to Tits' theorem that one can recover a group with a BN-pair as the group of type-preserving automorphisms of the associated building. We derive several group-theoretic consequences of this result.

Date received: May 7, 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-43.