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G^3, Special Session in Geometric Group Theory
January 10-13, 2001
part of the AMS/MAA joint meeting
New Orleans, LA, USA

Organizers
Phil Bowers, Martin Bridson, Stephen Brick, Jon Corson, Igor Mineyev

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Finiteness and CAT(0) properties of diagram groups
by
Daniel S. Farley
Penn State University

Given a semigroup presentation P and a positive word w in the generators of P, one can associate a group, called the diagram group over P based at w. Guba and Sapir have shown, for example, that Thompson's group F is the diagram group over < x | x=x2 > based at x.

In this talk an explicit construction of a contractible cubical free G-complex is given for any diagram group G. When P is a finite presentation, this complex is a proper CAT(0) space and the action of G is by isometries. If P is a finite presentation of a finite semigroup, then all diagram groups over P are of type F-infinity.

Date received: October 2, 2000

Copyright © 2000 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 # cafm-20.