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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Non-positively curved aspects of Artin groups of finite type

Mladen Bestvina

Geometry & Topology 3 (1999) 269–302

arXiv: math.GT/9812011

Abstract

Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we construct a space (simplicial complex) analogous to Teichmüller space that satisfies a weak nonpositive curvature condition and also a space “at infinity” analogous to the space of projective measured laminations. Using these constructs, we deduce several group-theoretic properties of Artin groups of finite type that are well-known in the case of braid groups.

Keywords
Artin groups, nonpositive curvature
Mathematical Subject Classification
Primary: 20F32, 20F36
Secondary: 55P20
References
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Publication
Received: 27 November 1998
Revised: 5 August 1999
Accepted: 5 September 1999
Published: 11 September 1999
Proposed: Walter Neumann
Seconded: Wolfgang Metzler, Joan Birman
Authors
Mladen Bestvina
Department of Mathematics
University of Utah
Salt Lake City
Utah 84112
USA