The grand arc graph
Speaker:
Yvon Verberne, Western University
Date and Time:
Wednesday, May 15, 2024 - 2:30pm to 3:30pm
Location:
The Fields Institute, Room 230
Abstract:
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.