Train track combinatorics and cluster algebras

2023/03/06 by Shunsuke Kano, Kano, Shunsuke
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2303.03190

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.

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