Volume 16, issue 1 (2012)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Small generating sets for the Torelli group

Andrew Putman

Geometry & Topology 16 (2012) 111–125
Abstract

Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup g of the genus g mapping class group has a finite generating set whose size grows cubically with respect to g. Our main tool is a new space called the handle graph on which g acts cocompactly.

Keywords
Torelli group, mapping class group
Mathematical Subject Classification 2010
Primary: 20F05
Secondary: 20F38, 57M07, 57N05
References
Publication
Received: 24 June 2011
Revised: 11 August 2011
Accepted: 1 November 2011
Published: 2 January 2012
Proposed: Joan Birman
Seconded: Danny Calegari, Ronald Stern
Authors
Andrew Putman
Department of Mathematics
Rice University, MS 136
6100 Main St
Houston
TX 77005
USA
http://www.math.rice.edu/~andyp/