Geometry & Topology

Small generating sets for the Torelli group

Andrew Putman

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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.

Article information

Source
Geom. Topol., Volume 16, Number 1 (2012), 111-125.

Dates
Received: 24 June 2011
Revised: 11 August 2011
Accepted: 1 November 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732380

Digital Object Identifier
doi:10.2140/gt.2012.16.111

Mathematical Reviews number (MathSciNet)
MR2872579

Zentralblatt MATH identifier
1296.57008

Subjects
Primary: 20F05: Generators, relations, and presentations
Secondary: 20F38: Other groups related to topology or analysis 57M07: Topological methods in group theory 57N05: Topology of $E^2$ , 2-manifolds

Keywords
Torelli group mapping class group

Citation

Putman, Andrew. Small generating sets for the Torelli group. Geom. Topol. 16 (2012), no. 1, 111--125. doi:10.2140/gt.2012.16.111. https://projecteuclid.org/euclid.gt/1513732380


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