The Grand Arc Graph -- A "curve graph" for infinite-type surfaces

Geometry Topology Seminar
Monday, March 14, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Assaf Bar-Natan – University of Toronto
Roberta Shapiro

In this talk, I will be defining the grand arc graph for infinite-type surfaces. This simplicial graph is motivated by the works of Fanoni-Ghaswala-McLeay, Bavard, and Bavard-Walker to define an infinite-type analogue of the curve graph. As in these earlier works, the grand arc graph is connected, (oftentimes) infinite-diameter, and (sometimes) delta hyperbolic. Moreover, the mapping class group acts on it by isometries, and the action is continuous on the visible boundary. If there's time, this talk will degenerate into open speculation about what the boundary looks like and what we can do with it.