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.

Keywords

Artin groups, nonpositive curvature

Mathematical Subject Classification

Primary: 20F32, 20F36

Secondary: 55P20

References

Forward citations

Publication

Received: 27 November 1998

Revised: 5 August 1999

Accepted: 5 September 1999

Published: 11 September 1999

Proposed: Walter Neumann

Seconded: Wolfgang Metzler, Joan Birman

Authors

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

Volume 3, issue 1 (1999)

Mladen Bestvina