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ISSN 1088-6834(e) ISSN 0894-0347(p)

The dimension of the Torelli group

Author(s): Mladen Bestvina; Kai-Uwe Bux; Dan Margalit
Journal: J. Amer. Math. Soc. 23 (2010), 61-105.
MSC (2000): Primary 20F34; Secondary 57M07
Posted: July 10, 2009
MathSciNet review: 2552249
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We prove that the cohomological dimension of the Torelli group for a closed, connected, orientable surface of genus $g \geq 2$ is equal to . This answers a question of Mess, who proved the lower bound and settled the case of . We also find the cohomological dimension of the Johnson kernel (the subgroup of the Torelli group generated by Dehn twists about separating curves) to be . For $g \geq 2$ , we prove that the top dimensional homology of the Torelli group is infinitely generated. Finally, we give a new proof of the theorem of Mess that gives a precise description of the Torelli group in genus 2. The main tool is a new contractible complex, called the ``complex of minimizing cycles'', on which the Torelli group acts.

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