Double Pants Decompositions of 2-surfaces
نویسندگان
چکیده
We consider the union of two pants decompositions of the same orientable 2-dimensional surface of any genus g. Each pants decomposition corresponds to a handlebody bounded by this surface, so two pants decompositions correspond to a Heegaard splitting of a 3manifold. We introduce a groupoid acting on double pants decompositions. This groupoid is generated by two simple transformations (called flips and handle twists), each transformation changing only one curve of the double pants decomposition. We prove that the groupoid acts transitively on all double pants decompositions corresponding to Heegaard splittings of a 3-dimensional sphere. As a corollary, we prove that the mapping class group of the surface is contained in the groupoid. 2000 Math. Subj. Class. 57M50.
منابع مشابه
Labeled Double Pants Decompositions
A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced by the authors. There are two natural operations acting on double pants decompositions: flips and handle-twists. It is shown by the authors that the groupoid generated by flips and handle-twists acts transitively on admissible double pants decompositions, where the class...
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