2010/08/22 by Anna Felikson, Felikson, Anna, S. M. Natanzon +2
Computer Science · Mathematics · #57M #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1008.3679
16 pages, many figures
arxiv created 2010/08/22 · openalex publication_date 2010/08/22 · arxiv updated 2010/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and handle twists acts transitively on admissible double pants decompositions where the class of admissible decompositions has a natural topological and combinatorial description. In this paper, we label the curves of double pants decompositions and show that for all but one surfaces the same groupoid acts transitively on all labeled admissible double pants decompositions. The only exclusion is a sphere with two handles, where the groupoid has 15 orbits.