Labeled double pants decompositions
Anna Felikson, Sergey Natanzon

TL;DR
This paper studies labeled double pants decompositions on surfaces, showing that a groupoid acts transitively on all but one specific case, revealing detailed symmetry properties of these decompositions.
Contribution
It extends previous work by labeling curves in double pants decompositions and analyzing the resulting groupoid action on these labeled structures.
Findings
Groupoid acts transitively on labeled decompositions for all but one surface
Sphere with two handles has 15 distinct orbits under the groupoid
Provides a detailed topological and combinatorial classification of labeled decompositions
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Advanced Combinatorial Mathematics
