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2017 On the second homology group of the Torelli subgroup of $\mathrm{Aut}(F_n)$
Matthew Day, Andrew Putman
Geom. Topol. 21(5): 2851-2896 (2017). DOI: 10.2140/gt.2017.21.2851

Abstract

Let IAn be the Torelli subgroup of Aut(Fn). We give an explicit finite set of generators for H2(IAn) as a GLn()–module. Corollaries include a version of surjective representation stability for H2(IAn), the vanishing of the GLn()–coinvariants of H2(IAn), and the vanishing of the second rational homology group of the level congruence subgroup of Aut(Fn). Our generating set is derived from a new group presentation for IAn which is infinite but which has a simple recursive form.

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Matthew Day. Andrew Putman. "On the second homology group of the Torelli subgroup of $\mathrm{Aut}(F_n)$." Geom. Topol. 21 (5) 2851 - 2896, 2017. https://doi.org/10.2140/gt.2017.21.2851

Information

Received: 22 October 2015; Revised: 8 November 2016; Accepted: 23 December 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06774935
MathSciNet: MR3687109
Digital Object Identifier: 10.2140/gt.2017.21.2851

Subjects:
Primary: 20E05, 20E36, 20F05, 20J06

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.21 • No. 5 • 2017
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