Hyperbolic features of two-dimensional Artin groups

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• Alexandre Martin (Heriot-Watt)
• Friday 17 May 2019, 13:45-14:45
• CMS, MR13.

If you have a question about this talk, please contact Richard Webb.

Artin groups form an interesting class of groups that generalise braid groups. There are many open problems about such groups, and in particular they are conjectured to be non-positively curved. For a two-dimensional Artin group whose associated Coxeter group is hyperbolic, we construct a universal acylindrical action on a hyperbolic complex, showing similarities with other classes of non-positively curved groups: mapping class groups, right-angled Artin groups, etc. We use the dynamics of this action to obtain certain structural properties of such Artin groups: strong form of the Tits alternative, classification of its maximal abelian subgroups, classification of its subgroups that virtually split as direct products. This is joint work with Piotr Przytycki.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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