Infinite-type surfaces and the omnipresent arcs by Tyrone Ghaswala

Geometry Topology Seminar
Monday, March 22, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Tyrone Ghaswala – CIRGET, Université du Québec à Montréal –
Roberta Shapiro

Please Note: A pre-talk will be given at 1 and office hours will be held at 3 (following the seminar talk).

In the world of finite-type surfaces, one of the key tools to studying the mapping class group is to study its action on the curve graph. The curve graph is a combinatorial object intrinsic to the surface, and its appeal lies in the fact that it is infinite-diameter and $\delta$-hyperbolic. For infinite-type surfaces, the curve graph disappointingly has diameter 2. However, all hope is not lost! In this talk I will introduce the omnipresent arc graph and we will see that for a large collection of infinite-type surfaces, the graph is infinite-diameter and $\delta$-hyperbolic. The talk will feature a new characterization of infinite-type surfaces, which provided the impetus for this project.

This is joint work with Federica Fanoni and Alan McLeay