Isomorphism Problems for Artin groups

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• Alexandre Martin, Heriot-Watt
• Friday 26 January 2024, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

Artin groups are a beautiful family of groups related to Coxeter groups, and defined by means of a presentation graph. The Isomorphism Problem asks when two different presentation graphs yield isomorphic groups. This problem has been well studied for Coxeter groups, but little is currently known for Artin groups. After reviewing this problem, I will focus on finding isomorphism invariants for Artin groups. In particular, a natural question is to ask whether the various families of Artin groups studied in the literature are well defined up to isomorphism. I will show that, unlike what happens for Coxeter groups, being of “large-type” is an isomorphism invariant for Artin groups. This is based on joint work with Nicolas Vaskou.

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

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