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BESTVINA, MLADEN; BUX, KAI-UWE; MARGALIT, DAN
Journal of the American Mathematical Society, 01/2010, Letnik: 23, Številka: 1Journal Article
We prove that the cohomological dimension of the Torelli group for a closed, connected, orientable surface of genus g \geq 2 is equal to 3g-5. This answers a question of Mess, who proved the lower bound and settled the case of g=2. 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 2g-3. 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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