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- W4300705589 abstract "We consider a union of two pants decompositions of the same orientable 2-dimensional surface of any genus g. Each pants decomposition corresponds to some handlebody bounded by this surface, so two pants decompositions correspond to a Heegaard splitting of a 3-manifold. We introduce a groupoid FT acting on double pants decompositions. This groupoid is generated by two simple transformations (called flips and handle twists), each transformation affecting only one curve of the double pants decomposition. We prove that FT acts transitively on all double pants decompositions corresponding to Heegaard splittings of a 3-dimensional sphere. As a corollary, the mapping class group is contained in FT." @default.
- W4300705589 created "2022-10-04" @default.
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- W4300705589 date "2010-05-01" @default.
- W4300705589 modified "2023-09-29" @default.
- W4300705589 title "Double pants decompositions of 2-surfaces" @default.
- W4300705589 doi "https://doi.org/10.48550/arxiv.1005.0073" @default.
- W4300705589 hasPublicationYear "2010" @default.
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