Math Colloquium: What is... a mapping class group? (series unlisted)

Abstract: A mapping class group of a surface is the group of isotopy classes of homeomorphisms of the surface. These groups play a crucial role in low-dimensional topology, as many topological objects can be constructed out of the information of a surface and a homeomorphism on that surface. The famous and useful Nielsen-Thurston Classification theorem characterizes these homeomorphisms as long as surfaces have finitely generated fundamental group. When surfaces do not have finitely generated fundamental group, their mapping class groups are called "big" and are less well understood. I will explain this background and discuss some of my recent joint work in the area of mapping class groups. In particular I'll give an example of a novel homeomorphism in big mapping class groups that has unusual dynamics. ​

Mathematics

Audience: undergraduates

Brooklyn College Math Department Events

Series comments: The Brooklyn College Math Department hosts a lot great events for undergraduates and faculty! These events are organized by The Math Club, The Putnam Club, and faculty in the Math Department.