Geometry & Topology

Towards representation stability for the second homology of the Torelli group

Søren K Boldsen and Mia Hauge Dollerup

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Abstract

We show for g7 that the second homology group of the Torelli group, H2(g,1;), is generated as an Sp(2g,)–module by the image of H2(6,1;) under the stabilization map. In the process we also show that the quotient B(Fg,i;i)g,i by the Torelli group of the complex of arcs with identity permutation is (g2)–connected for i=1,2.

Article information

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

Dates
Received: 4 September 2011
Accepted: 14 March 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 20C12: Integral representations of infinite groups 20J06: Cohomology of groups

Keywords
representation stability Torelli group

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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