February 12, 2020
Math Tower P-131
|Brandon Gontmacher, Stony Brook University|
Dehn Twists and the Mapping Class Group
The use of algebra - in particular, group theory - to understand the topology and geometry of a space is the goal of geometric group theory. At the heart of this is the mapping class group, which tells us about the maps from a space to itself. In particular, elements of the mapping class group called Dehn twists play a central role and are some of the best understood types of maps. We will focus on surfaces (2-manifolds), and specifically will look at the torus as a toy example throughout.