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


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.