Train track combinatorics and cluster algebras
Geometric Topology
2023-03-07 v1 Combinatorics
Abstract
The concepts of train track was introduced by W. P. Thurston to study the measured foliations/laminations and the pseudo-Anosov mapping classes on a surface. In this paper, we translate some concepts of train tracks into the language of cluster algebras using the Goncharov--Shen's potential function [GS15]. Through this translation, we prove the sign stability [IK21] of the general pseudo-Anosov mapping classes.
Cite
@article{arxiv.2303.03190,
title = {Train track combinatorics and cluster algebras},
author = {Shunsuke Kano},
journal= {arXiv preprint arXiv:2303.03190},
year = {2023}
}
Comments
42 pages, 23 figures