Geometry & Topology, Vol. 3 (1999)
Paper no. 12, pages 269--302.
Non-positively curved aspects of Artin groups of finite type
Mladen Bestvina
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
Teichmueller 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
AMS subject classification.
Primary: 20F32, 20F36.
Secondary: 55P20.
DOI: 10.2140/gt.1999.3.269
E-print: arXiv:math.GT/9812011
Submitted to GT on 27 November 1998.
(Revised 5 August 1999.)
Paper accepted 5 September 1999.
Paper published 11 September 1999.
Notes on file formats
Mladen Bestvina
Department of Mathematics, University of Utah
Salt Lake City, UT 84112, USA
Email: bestvina@math.utah.edu
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