Transfinite mutations in the completed infinity-gon

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:155

Article

关键词: Cluster algebras;    Triangulated surfaces;    Mutation;   

DOI  :  10.1016/j.jcta.2017.11.011

来源: Elsevier

【 摘 要 】

We introduce mutation along infinite admissible sequences for infinitely marked surfaces, that is surfaces with infinitely many marked points on the boundary. We show that mutation along such admissible sequences produces a preorder on the set of triangulations of a fixed infinitely marked surface. We provide a complete classification of the strong mutation equivalence classes of triangulations of the infinity-gon and the completed infinity-gon respectively, where strong mutation equivalence is the equivalence relation induced by this preorder. Finally, we introduce the notion of transfinite mutations in the completed infinity-gon and show that all its triangulations are transfinitely mutation equivalent, that is we can reach any triangulation of the completed infinity-gon from any other triangulation via a transfinite mutation. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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