Towards representation stability for the second homology of the Torelli group

Boldsen, Søren K; Dollerup, Mia Hauge

doi:10.2140/gt.2012.16.1725

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Towards representation stability for the second homology of the Torelli group

Søren K Boldsen and Mia Hauge Dollerup

Geometry & Topology 16 (2012) 1725–1765

DOI: 10.2140/gt.2012.16.1725

Abstract

We show for $g \geq 7$ that the second homology group of the Torelli group, $H_{2} (ℐ_{g, 1}; ℚ)$ , is generated as an $Sp (2 g, ℤ)$ –module by the image of $H_{2} (ℐ_{6, 1}; ℚ)$ under the stabilization map. In the process we also show that the quotient $B (F_{g, i}; i) ∕ ℐ_{g, i}$ by the Torelli group of the complex of arcs with identity permutation is $(g - 2)$ –connected for $i = 1, 2$ .

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Keywords

representation stability, Torelli group

Mathematical Subject Classification 2010

Primary: 20C12, 20J06

References

Publication

Received: 4 September 2011

Accepted: 14 March 2012

Published: 3 August 2012

Proposed: Benson Farb

Seconded: Danny Calegari, Jesper Grodal

Authors

Søren K Boldsen
Mathematical Institute University of Bonn Endenicher Allee 60 D-53115 Bonn Germany

Mia Hauge Dollerup
Department of Mathematics Aarhus University Klokkerfaldet 109 DK-8210 Aarhus Denmark

Volume 16, issue 3 (2012)