## Geometry & Topology

### Non-positively curved aspects of Artin groups of finite type

#### 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.

#### Article information

Source
Geom. Topol., Volume 3, Number 1 (1999), 269-302.

Dates
Revised: 5 August 1999
Accepted: 5 September 1999
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883148

Digital Object Identifier
doi:10.2140/gt.1999.3.269

Mathematical Reviews number (MathSciNet)
MR1714913

Zentralblatt MATH identifier
0998.20034

Subjects
Primary: 20F32 20F36: Braid groups; Artin groups
Secondary: 55P20: Eilenberg-Mac Lane spaces

#### Citation

Bestvina, Mladen. Non-positively curved aspects of Artin groups of finite type. Geom. Topol. 3 (1999), no. 1, 269--302. doi:10.2140/gt.1999.3.269. https://projecteuclid.org/euclid.gt/1513883148

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