Small generating sets for the Torelli group
arXiv:1106.3294 · doi:10.2140/gt.2012.16.111
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 called the handle graph on which the Torelli group acts cocompactly.
12 pages, 3 figures; serious revision; to appear in Geom. Topol