Katherine Goldman
McGill University
Title
Residual properties of 2-dimensional Artin groups
Abstract
It is a longstanding open question to determine which Artin groups are residually finite. Past results have followed from linearity (e.g., for spherical-type) or product decompositions in rank 3. We present a new approach to this problem using intermediate quotients to so-called Shephard groups. These Shephard groups possess their own interesting (and sometimes counterintuitive) geometry which we can leverage to give new information about their corresponding Artin groups in some cases. As a highlight of this connection, we show that an Artin group which is simultaneously 2-dimensional, hyperbolic-type, and FC-type is residually finite. One of the key features of the proof we will discuss is the fact that hyperbolic-type 2-dimensional Shephard groups are relatively hyperbolic, which is almost never true of Artin groups.
