Geometry & Topology
- Geom. Topol.
- Volume 3, Number 1 (1999), 269-302.
Non-positively curved aspects of Artin groups of finite type
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.
Geom. Topol., Volume 3, Number 1 (1999), 269-302.
Received: 27 November 1998
Revised: 5 August 1999
Accepted: 5 September 1999
First available in Project Euclid: 21 December 2017
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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