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Topics in Geometric Group Theory |
| November 05, 2007 to November 09, 2007 |
| Organized By: Noel Brady, Mike Davis, Mark Feighn |
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| Parent Programs: |
| Geometric Group Theory |
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| Return to Workshop Description |
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Dimension of Torelli groups
Wednesday November 7, 2007
10:30AM - 11:20AM
Speakers:
Dan Margalit
Abstract:
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.
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