Department of Mathematics

Speaker: Dan Margalit
Title: Mapping Class Groups and Torelli Groups
Affiliation: Georgia Tech
Date: Friday, March 4, 2011
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. The mapping class group encodes the symmetries of a topological surface. This group was first studied by Max Dehn in the 1920's. The subject of mapping class groups has become an extremely active area of research in the past few decades, in large part due to the work of Birman and of Thurston. I will give an introduction to the subject, explaining some of the key techniques. One of the important tools for studying the mapping class group is its symplectic representation. The kernel of this representation, the Torelli group, is not very well understood. I will explain a new combinatorial approach to studying the Torelli group, and explain some theorems obtained with Mladen Bestvina and Kai-Uwe Bux. For example, I will show that the cohomological dimension of the Torelli group of a genus g >= 2 surface is 3g-5.