Ideal Triangulations of Pseudo-Anosov Mapping Tori

TL;DR

This paper presents a method to construct ideal triangulations of pseudo-Anosov mapping tori, introducing a new conjugacy invariant and providing an alternative proof of a known theorem, based on ideas from Hamenstadt.

Contribution

It introduces a novel construction of ideal triangulations for pseudo-Anosov mapping tori and defines a new conjugacy invariant of mapping classes.

Findings

Constructed ideal triangulations for pseudo-Anosov mapping tori.

Established a new conjugacy invariant for mapping classes.

Provided a new proof of Farb-Leininger-Margalit's theorem.

Abstract

We show how to construct an ideal triangulation of a mapping torus of a pseudo-Anosov map punctured along the singular fibers. This gives rise to a new conjugacy invariant of mapping classes, and a new proof of a theorem of Farb-Leininger-Margalit. The approach in this paper is based on ideas of Hamenstadt.