关于带孔和捏合曲面的不可约三角剖分
组合数学
2013-06-04 v2 一般拓扑
几何拓扑
历史与综述
摘要
如果一个带孔或捏合曲面的三角剖分在不产生多重边或不改变曲面拓扑类型的情况下无法收缩任何边，则称其为不可约的。我们确立了任意带孔曲面的（非同构）不可约三角剖分集合的有限性。确定了 M\"obius 带（共 6 个）和捏合环面（共 2 个）的不可约三角剖分的完整列表。确定了具有最多 8 个顶点的射影平面三角剖分的所有非同构组合类型（共 20 个）。
引用
@article{arxiv.1207.2800,
title = {On irreducible triangulations of punctured and pinched surfaces},
author = {M. J. Chávez and S. Lawrencenko and A. Quintero and M. T. Villar},
journal= {arXiv preprint arXiv:1207.2800},
year = {2013}
}
备注
This paper has been withdrawn by the authors because the proof of Lemma 3.3 has a gap. More precisely, the claim "If R has a pylonic vertex, v, incident with at least two cables, the pylonicity of v is destroyed by the splitting of any corner", as stated, is unjustified and looks false in whole generality; the authors overlooked some cases