Volume 16, issue 1 (2012)

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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 ${\mathsc{ℐ}}_{g}$ 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 ${\mathsc{ℐ}}_{g}$ acts cocompactly.

Keywords
Torelli group, mapping class group
Mathematical Subject Classification 2010
Primary: 20F05
Secondary: 20F38, 57M07, 57N05