A curve graph for Artin groups

Geometry Topology Seminar
Monday, September 13, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Rose Morris-Wright – UCLA – rose@math.ucla.eduhttps://www.rosemorriswright.com/
Beibei Liu

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Artin groups are a generalization of braid groups, first defined by Tits in the 1960s. While specific types of Artin groups have many of the same properties as braid groups, other examples of Artin groups are still very mysterious. Braid groups are can be thought of as the mapping class groups of a punctured disc. The combinatorial and geometric structure of the mapping class group is reflected in a Gromov-hyperbolic space called the curve graph of the mapping class group. Using the curve graph of the mapping class group of a punctured disc, we can define a graph associated to a given braid group. In this talk, I will discuss how to generalize this construction to more general classes of Artin groups. I will also discuss the current known properties of this graph and further open questions about what properties of the curve graph carry over to this new graph.