2006/04/30 by Joseph Maher
Mathematics · #math.GT #math.GR #msc:37E30 #msc:20F65 #msc:57M50
paper · pdf · doi:10.1215/00127094-2010-216
published as Duke Math. J. 156, no. 3 (2011), 429-468 · 31 pages, 7 figures. v2: Added references to work of Rivin and I. Kapovich. v3: This version now only contains the mapping class group results. The original application to 3-manifolds contained a gap, which is fixed in arXiv:0809.4881. v4: revised version
arxiv created 2010/11/18 · arxiv updated 2019/12/19
We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.