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arxiv 1101.5767 v2 pith:7WLKQRHB submitted 2011-01-30 math.AT math.RT

Towards representation stability for the second homology of the Torelli group

S{\o}ren K. Boldsen , Mia Hauge Dollerup This is my paper
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 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Finite generation, algebraicity, and representation stability for homology of Torelli groups

    math.GT 2026-06 unverdicted novelty 8.0

    Proves finite generation of H_k(I_g; Z) for k ≤ g-2 and that rational homology is an algebraic Sp(2g,Z)-representation, turning conditional cohomology computations into theorems and proving Morita's conjecture.

  2. 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.