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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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Artin groups of finite type
by
Mladen Bestvina
University of Utah

It is an open question whether Artin groups of finite type (e.g. braid groups) act cocompactly and discretely on a CAT(0) space by isometries. In this talk I will point out a property that these groups satisfy, that is substantially weaker than CAT(0), but suffices to deduce the desired group-theoretic consequences. Applications include:

  1. Finite subgroups of the quotient by \Delta2 are cyclic.

  2. Translation lengths are bounded away from 0; thus abelian subgroups are finitely generated.

  3. A new proof of Squier's theorem that they are duality groups.
If time permits, I will describe the joint work in progress with Mark Feighn that develops an algorithm for finding axes of elements.

Date received: April 17, 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-27.