Towards representation stability for the second homology of the Torelli group

Details Towards representation stability for the second homology of the Torelli group Towards representation stability for the second homology of the Torelli group

2011-01-30

arxiv.org/abs/1101.5767v2

Mathematics

Algebraic Topology

36 pages

Scientific paper

We show for g > 6 that the second homology group of the Torelli group of a surface of genus g and 1 boundary component is generated as an Sp(2g,Z)-module by the image under the stabilization map of the second homology group of the Torelli group of a surface of genus 6 and 1 boundary component. In the process we also show that the quotient of the complex of arcs with identity permutation by the Torelli group is (g-2)-connected, for one or two boundary components.

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