Chathumini Kondasinghe, Temple University
Event Date
2026-03-14
Event Time
01:00 pm ~ 02:00 pm
Event Location
617 Wachman Hall
In this talk I will introduce the mapping class group of a surface. Informally, it is the group of isotopy classes of orientation preserving diffeomorphisms of a surface, which is a fundamental object in surface theory.
After briefly discussing surfaces and their homeomorphisms, I will define the mapping class group, look at several examples, and talk about some interesting properties of it. I will then explain the Nielsen–Thurston classification theorem, which says that for a surface of genus greater than 1 (possibly with punctures), every mapping class is either periodic, reducible, or pseudo-Anosov. I will finish by discussing pseudo-Anosov mapping classes, which exhibit particularly interesting dynamical behavior.