2014/06/29 by Fang Li, Li, Fang, Jichun Liu +3
Mathematics · #05C10 #05E10 #05E15 #13F60 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT) #math.GT #math.RT #msc:05C10 #msc:05E10 #msc:05E15 #msc:13F60
paper · pdf · doi:10.48550/arxiv.1406.7493
14 pages, 17 figures, Pacific Journal of Mathematics, 2014. arXiv admin note: text overlap with arXiv:math/0608367 by other authors
arxiv created 2014/06/29 · openalex publication_date 2014/06/29 · arxiv updated 2014/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the distribution of the genuses of cluster quivers of finite mutation type. First, we prove that in the 11 exceptional cases, the distribution of genuses is 0 or 1. Next, we consider the relationship between the genus of an oriented surface and that of cluster quivers from this surface. It is verified that the genus of an oriented surface is an upper bound for the genuses of cluster quivers from this surface. Furthermore, for any non-negative integer n and a closed oriented surface of genus n, we show that there always exist a set of punctures and a triangulation of this surface such that the corresponding cluster quiver from this triangulation is exactly of genus n.