In joint work with Mladen Bestvina and Kai-Uwe Bux, we prove
that the cohomological dimension of the Torelli group for a
surface of genus g at least 2 is 3g-5 (answering a question
of Mess), and that the top dimensional homology is
infinitely generated. We show that the subgroup generated
by Dehn twists about separating curves has cohomological
dimension 2g-3. We also give a new proof of the theorem of
Mess which states that the genus 2 Torelli group is an
infinitely generated free group. The main tool is a new
contractible complex, called the "complex of cycles", on
which the Torelli group acts.

Lecture #12577

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