论文标题
多个Alexandrov空间的粘合
Gluing of multiple Alexandrov spaces
论文作者
论文摘要
在本文中，我们讨论了将多个Alexandrov空间粘在Alexandrov空间的足够和必要条件。我们提出了一个粘合的猜想，该猜想说，当且仅当粘合到沿边界的路径均衡时，Alexandrov空间的有限粘合是Alexandrov的空间，并且将切线锥粘合到Alexandrov空间。这概括了Petrunin的胶合定理。在粘合猜想的假设下，我们将$ 2 $ - 点粘在$（n-1，ε）$ - 常规点上的胶水分类为本地可分开的胶合，并且接近未粘合的$（n-1，ε）$ - 常规点 - 常规点为本地涉嫌粘合。我们还证明，如果$（n-1，ε）$ - 常规点在胶合边界中是离散的，则粘合猜想是正确的。特别是，这意味着一般的粘合猜想以及维度2中的新粘合定理。
In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov space, if and only if the gluing is by path isometry along the boundaries and the tangent cones are glued to Alexandrov spaces. This generalizes Petrunin's Gluing Theorem. Under the assumptions of the Gluing Conjecture, we classify the $2$-point gluing over $(n-1,ε)$-regular points as local separable gluing and the gluing near un-glued $(n-1,ε)$-regular points as local involutional gluing. We also prove that the Gluing Conjecture is true if the complement of $(n-1,ε)$-regular points is discrete in the glued boundary. In particular, this implies the general Gluing Conjecture as well as a new Gluing Theorem in dimension 2.
