Towards representation stability for the second homology of the Torelli group
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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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Calculating the second rational cohomology group of the Torelli group
An exposition of the calculation of the second rational cohomology group of the Torelli group using the Johnson homomorphism and two key prior results.
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