Problems and progress in understanding the Torelli group (Benson Farb)

Abstract:

The Torelli group T(S) is defined to be the subgroup of the mapping class group consisting of those mapping classes acting trivially on H_1(S,Z). The study of T(S) connects to 3-manifold theory, symplectic representation theory, combinatorial group theory, and algebraic geometry. In this talk I will describe some of the main themes in this beautiful topic, concentrating on the combinatorial and (co)homological aspects. I will also describe some recent progress in this direction, as well as a number of open questions and conjectures. Different parts of the talk will describe joint work with (separately) Daniel Biss, Nick Ivanov, and Tara Brendle.