Asymptotic triangulations and Coxeter transformations of the annulus

TL;DR

This paper introduces an algebraic and combinatorial approach to asymptotic triangulations of the annulus using Coxeter transformations, providing new insights into their structure and limits.

Contribution

It offers an alternative method to construct asymptotic triangulations of the annulus through Coxeter transformations, linking geometric limits with algebraic and combinatorial frameworks.

Findings

Coxeter transformations can generate asymptotic triangulations

The approach connects geometric limits with algebraic structures

Provides a new framework for studying limits of triangulations

Abstract

Asymptotic triangulations can be viewed as limits of triangulations under the action of the mapping class group. In the case of the annulus, such triangulations have been introduced by Baur and Dupont. We construct an alternative method of obtaining these asymptotic triangulations using Coxeter transformations. This provides us with an algebraic and combinatorial framework for studying these limits via the associated quivers.