Non-positively curved aspects of Artin groups of finite type

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

1998-12-01

arxiv.org/abs/math/9812011v2

Geom. Topol. 3 (1999), 269-302

Mathematics

Geometric Topology

34 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper12.abs.html

Scientific paper

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.

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