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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
Abstract

We show for g 7 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.

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