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 virtually cocompact special Artin groups) 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.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

[[Please provide your first and last name so that the speaker can identify you. Kindly submit your questions or comments using the chat box, not via audio.]]

The livestream is on Zoom at uqam.zoom.us/j/88383789249 It is recommended to subscribe to the CIRGET newsletter. Please send an email to haedrich.alexandra@uqam.ca , providing your name and affiliation.

Some talks can be seen at www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA