Asymptotic Triangulations and Coxeter Transformations of the Annulus

Abstract

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 in K. Baur and G. Dupont (Compactifying exchange graphs: Annuli and tubes, Ann. Comb. 3(18) (2014), 797-839). 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.2010 Mathematics Subject Classification. 16G20, 20F55, 13F60.

Admissible Homomorphisms and Equivariant Relations Between Weighted Projective Lines

“…In this paper, we consider curves and arcs up to homotopy. The following definition refers to [11,47].…”