与三角剖分曲面相关的带势箭图，第四部分：去除边界假设
组合数学
2015-10-27 v5
摘要
我们证明与带标记点的曲面（可能空边界）的三角剖分相关的带势箭图是非退化的，前提是带标记点的曲面不是恰好有5个穿孔的闭球面。这是通过明确定义对应于标记三角剖分的QP，并证明每当两个标记三角剖分通过翻转相关联时，它们的QP通过相应的QP突变相关联来完成的。作为副产品，对于（任意穿孔的）非空边界曲面，我们得到了相关QP的非退化性的证明，该证明独立于作者在本系列第一篇论文中给出的证明。用于证明翻转和QP突变之间上述兼容性的主要工具是我们所称的"Popping定理"，粗略地说，该定理指出，来自具有自折叠三角形的理想三角剖分的势中明显缺乏对称性可以通过适当的右等价来修复。
引用
@article{arxiv.1206.1798,
title = {Quivers with potentials associated to triangulated surfaces, part IV: Removing boundary assumptions},
author = {Daniel Labardini-Fragoso},
journal= {arXiv preprint arXiv:1206.1798},
year = {2015}
}
备注
v5: Final version. Published by Selecta Mathematica (New Series). Published version contains a few minor redaction errors. E.g., "related by a flip" and "related by a QP-mutation" were incorrectly replaced by "related to a flip" and "related to a QP-mutation" therein. Changes following suggestions by the referee. 36 pages, 21 figures. Dedicated to the memory of Professor Andrei Zelevinsky