GENUSES OF CLUSTER QUIVERS OF FINITE MUTATION TYPE

被引：5

作者：

Li, Fang ^{[1
]}

Liu, Jichun ^{[1
,2
]}

Yang, Yichao ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[2] Fujian Jiangxia Univ, Dept Math & Phys, Fuzhou 350108, Peoples R China

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2014年 / 269卷 / 01期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

cluster quiver; finite mutation type; genus; triangulation of surface; ALGEBRAS;

D O I：

10.2140/pjm.2014.269.133

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 nonnegative 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.

引用

页码：133 / 148

页数：16

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