### A Deligne Complex for Artin Monoids (Based on joint work with Rachael Boyd and Ruth Charney)

Geometry and Topology Seminar

9th February 2021, 4:00 pm – 5:00 pm

Zoom seminar, if interested, please email one of the organisers to gain access to the Zoom link

I will introduce a geometric construction associated to an Artin monoid. Artin groups are a generalization of braid groups and the Artin monoid is the monoid with the same generators and relations as in the Artin group. In 1995, Charney and Davis introduced the Deligne complex, a CAT(0) cube complex, which they use to prove the K(pi,1) conjecture for FC type Artin groups. In a recent paper, Boyd, Charney and I use Boyd’s construction of a monoid coset for an Artin monoid to create a version of the Deligne complex for an Artin monoid.

In this talk, I will first discuss Artin monoids, how they differ from Artin groups, and why Artin monoids are interesting objects to study. Then I will outline the construction of the Deligne complex for an Artin monoid. Finally I will discuss some of the geometric properties of this complex that we have derived, including the fact that the Deligne complex of a monoid is always contractible, with a locally isometric embedding into the Deligne complex of the group.

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