Genuses of cluster quivers of finite mutation type

Fang Li; Jichun Liu; Yichao Yang

Genuses of cluster quivers of finite mutation type

Representation Theory 2014-07-01 v1 Geometric Topology

Authors: Fang Li , Jichun Liu , Yichao Yang

Abstract

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 $n$ .

Keywords

cluster quivers finite mutation type genus oriented surface triangulation punctures exceptional cases

Cite

@article{arxiv.1406.7493,
  title  = {Genuses of cluster quivers of finite mutation type},
  author = {Fang Li and Jichun Liu and Yichao Yang},
  journal= {arXiv preprint arXiv:1406.7493},
  year   = {2014}
}

Comments

14 pages, 17 figures, Pacific Journal of Mathematics, 2014. arXiv admin note: text overlap with arXiv:math/0608367 by other authors

Genuses of cluster quivers of finite mutation type

Abstract

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