Big mapping class groups and rigidity of the simple circle by Lvzhou Chen

Geometry Topology Seminar
Monday, March 15, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Lvzhou Chen – UT Austin – lvzhou.chen@math.utexas.edu
Roberta Shapiro

Please Note: Office hours will be held 3-4 pm.

Surfaces of infinite type, such as the plane minus a Cantor set, occur naturally in dynamics. However, their mapping class groups are much less studied and understood compared to the mapping class groups of surfaces of finite type. Many fundamental questions remain open. We will discuss the mapping class group G of the plane minus a Cantor set, and show that any nontrivial G-action on the circle is semi-conjugate to its action on the so-called simple circle. Along the way, we will discuss some structural results of G to address the following questions: What are some interesting subgroups of G? Is G generated by torsion elements? This is joint work with Danny Calegari.