Small generating sets for the Torelli group - [pdf] [ps]
Geom. Topol. 16 (2012), 111–125.

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