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Asymptotic triangulations can be viewed as limits of triangulations under theaction of the mapping class group. In the case of the annulus, suchtriangulations have been introduced by Baur and Dupont. We construct analternative method of obtaining these asymptotic triangulations using Coxetertransformations. This provides us with an algebraic and combinatorial frameworkfor studying these limits via the associated quivers.

Asymptotic triangulations and Coxeter transformations of the annulus