An Infinite Presentation of the Torelli Group
An Infinite Presentation of the Torelli Group
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Torelli 集团的无限展示
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Andrew Putman
中科院分区：
文献类型：
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作者：
Andrew Putman
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.
