Mathematics – Geometric Topology
Scientific paper
2007-03-19
Geom. Funct. Anal. 19 (2009), no. 2, 591-643.
Mathematics
Geometric Topology
52 pages, 14 figures, 1 table, very heavily revised and expanded, section on obtaining presentations from group actions spun o
Scientific paper
In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all "separating twists", all "bounding pair maps", and all "commutators of simply intersecting pairs" and whose relations all come from a short list of topological configurations of these generators on the surface. Aside from a few obvious ones, all of these relations come from a set of embeddings of groups derived from surface groups into the Torelli group. In the process of analyzing these embeddings, we derive a novel presentation for the fundamental group of a closed surface whose generating set is the set of all simple closed curves.
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