English

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

R2 v1 2026-06-28T09:03:34.199Z