Volume 21, issue 5 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
On the second homology group of the Torelli subgroup of $\mathrm{Aut}(F_n)$

Matthew Day and Andrew Putman

Geometry & Topology 21 (2017) 2851–2896
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.

Keywords
automorphism group of free group, Torelli group
Mathematical Subject Classification 2010
Primary: 20E05, 20E36, 20F05, 20J06
Supplementary material

GAP code for the calculations

References
Publication
Received: 22 October 2015
Revised: 8 November 2016
Accepted: 23 December 2016
Published: 15 August 2017
Proposed: Shigeyuki Morita
Seconded: Benson Farb, Mark Behrens
Authors
Matthew Day
Department of Mathematical Sciences
University of Arkansas
Fayetteville, AR
United States
Andrew Putman
Department of Mathematics
University of Notre Dame
Notre Dame, IN
United States