论文标题
$ g_2 $ - 最小的正常3 peudomanifolds的特征最多四个奇异性
A characterization of $g_2$-minimal normal 3-pseudomanifolds with at most four singularities
论文作者
论文摘要
令$δ$为$ g_2 $ - 最小的正常3张immanifold。 $δ$的顶点，其链接不是一个球体称为单数顶点。当$δ$最多包含两个单数顶点时，其组合表征是已知的[9]。在本文中，当它具有三个单数顶点时（包括一个$ \ mathbb {rp}^2 $ singularity或四个单数顶点，包括两个$ \ mathbb {rp}^2 $ singullities时，我们会介绍这种$δ$的组合表征。在这两种情况下，我们都证明了$δ$是从表面的单位悬浮液中获得的，并且通过应用类型连接的总和，顶点折叠和边缘折叠的类型的组合操作来实现$ 4 $ simplices的某些边界复合物。
Let $Δ$ be a $g_2$-minimal normal 3-pseudomanifold. A vertex in $Δ$ whose link is not a sphere is called a singular vertex. When $Δ$ contains at most two singular vertices, its combinatorial characterization is known [9]. In this article, we present a combinatorial characterization of such a $Δ$ when it has three singular vertices, including one $\mathbb{RP}^2$-singularity, or four singular vertices, including two $\mathbb{RP}^2$-singularities. In both cases, we prove that $Δ$ is obtained from a one-vertex suspension of a surface, and some boundary complexes of $4$-simplices by applying the combinatorial operations of types connected sums, vertex foldings, and edge foldings.
