THE DIMENSION OF THE TORELLI GROUP

By M. Bestvina, Kai-Uwe Bux, Dany Margalit. 2007

51 citations recorded by the source corpus.

We prove that the cohomological dimension of the Torelli group for a closed, connected, orientable surface of genus g � 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 � 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b1fb65fcef3b5c55b2dbaa2bea17ebea317eb902

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Citations in the corpus

Representation theory and homological stability (2010, methodology): “it [BBM1] span an inﬁnitedimensional subspace, but as a GLn Z–module this is a permutation module generated by a single element; similarly, the classes in H3g−2(Ig,1;Q) found by Bestvina–Bux–Margalit [BBM2] span a cyclic Sp2g Z–module. In particular, the action of GLn Z or Sp2g Z on such a subspace ”
Stable commutator length on mapping class groups (2013, methodology): “— We thank Danny Calegari for his interest and to Dan Margalit for pointing us to the reference [6].”