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Small generating sets for the Torelli group

Andrew Putman
Geometry & Topology 16 (2012) 111–125
DOI: 10.2140/gt.2012.16.111
Abstract

Proving a conjecture of Dennis Johnson, we show that the Torelli subgroup ℐg 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 ℐg 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/