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.

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Mladen Bestvina
Department of Mathematics, University of Utah
Salt Lake City, UT 84112, USA

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