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arxiv: 1101.5767 · v2 · submitted 2011-01-30 · 🧮 math.AT · math.RT

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Towards representation stability for the second homology of the Torelli group

S{\o}ren K. Boldsen , Mia Hauge Dollerup
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classification 🧮 math.AT math.RT
keywords grouptorelliboundaryhomologysecondcomponentgenussurface
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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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Cited by 1 Pith paper

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  1. Calculating the second rational cohomology group of the Torelli group

    math.GT 2026-04 unverdicted novelty 2.0

    An exposition of the calculation of the second rational cohomology group of the Torelli group using the Johnson homomorphism and two key prior results.