Dynamics Seminar

Event Information The grand arc graph
14:10 on Monday November 28, 2022
15:00 on Monday November 28, 2022
BA6183, Bahen Center, 40 St. George St.
Yvon Verberne

University of Toronto

One of the key tools to study surfaces of finite-type is the curve graph. Masur and Minsky showed that the curve graph is both infinite diameter and Gromov hyperbolic. Additionally, Masur and Minsky showed the curve graph’s utility by using it to study the geometry of the mapping class group for surfaces of finite-type. Unfortunately, for surfaces of infinite-type the curve graph has diameter 2. In this talk, we introduce the grand arc graph and show that for large collections of infinite-type surfaces, the grand arc graph has infinite diameter and is Gromov hyperbolic. This work is joint with Assaf Bar-Natan.