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arXiv · 1101.5767

Towards representation stability for the second homology of the Torelli group

Søren K. Boldsen·Mia Hauge Dollerup
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Abstract

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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Søren K. Boldsen, Mia Hauge Dollerup. 2011-01-30. Towards representation stability for the second homology of the Torelli group. https://arxiv.org/abs/1101.5767

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