Towards representation stability for the second homology of the Torelli group

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On the second homology group of the Torelli subgroup of AutpFnq

Let IAn be the Torelli subgroup of AutpFnq. We give an explicit finite set of generators for H2pIAnq as a GLnpZq-module. Corollaries include a version of surjective representation stability for H2pIAnq, the vanishing of the GLnpZq-coinvariants of H2pIAnq, and the vanishing of the second rational homology group of the level l congruence subgroup of AutpFnq. Our generating set is derived from a n...

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ژورنال

عنوان ژورنال: Geometry & Topology

سال: 2012

ISSN: 1364-0380,1465-3060

DOI: 10.2140/gt.2012.16.1725