Small generating sets for the Torelli group

Putman, Andrew

doi:10.2140/gt.2012.16.111

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

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 $ℐ_{g}$ 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 $ℐ_{g}$ 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/

Volume 16, issue 1 (2012)