## Geometry & Topology

### Towards representation stability for the second homology of the Torelli group

#### Abstract

We show for $g≥7$ that the second homology group of the Torelli group, $H2(ℐg,1;ℚ)$, is generated as an $Sp(2g,ℤ)$–module by the image of $H2(ℐ6,1;ℚ)$ under the stabilization map. In the process we also show that the quotient $B(Fg,i;i)∕ℐg,i$ by the Torelli group of the complex of arcs with identity permutation is $(g−2)$–connected for $i=1,2$.

#### Article information

Source
Geom. Topol., Volume 16, Number 3 (2012), 1725-1765.

Dates
Accepted: 14 March 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732447

Digital Object Identifier
doi:10.2140/gt.2012.16.1725

Mathematical Reviews number (MathSciNet)
MR2967062

Zentralblatt MATH identifier
1282.20053

#### Citation

Boldsen, Søren K; Dollerup, Mia Hauge. Towards representation stability for the second homology of the Torelli group. Geom. Topol. 16 (2012), no. 3, 1725--1765. doi:10.2140/gt.2012.16.1725. https://projecteuclid.org/euclid.gt/1513732447

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