论文标题
可定位$ 3 $ manifolds的规范几何化，由$ 3 $ - polytopes的矢量色定义
Canonical geometrization of orientable $3$-manifolds defined by vector-colourings of $3$-polytopes
论文作者
论文摘要
简而言之，瑟斯顿（G.〜Perelman最终证明）表示，任何面向的$ 3 $ - manifold都可以将构成分区分为零件，这是八种类型之一的几何结构。在开创性的论文（1991）中，Januszkiewicz引入了宽类$ n $ dimensional歧管 - 简单的$ n $ polytopes上的小封面。我们对以下问题给出了完整的答案：为任何可取向的$ 3 $ manifold构建明确的规范分解，这是由简单$ 3 $ - 多型托管的矢量色所定义的，尤其是对于小封面。证明是基于对不同作者之前获得的结果的分析。
In short geometrization conjecture of W.\,Thurston (finally proved by G.~Perelman) says that any oriented $3$-manifold can be canonically partitioned into pieces, which have a geometric structure of one of the eight types. In the seminal paper (1991) M.\,W.\,Davis and T.\,Januszkiewicz introduced a wide class of $n$-dimensional manifolds -- small covers over simple $n$-polytopes. We give a complete answer to the following problem: to build an explicit canonical decomposition for any orientable $3$-manifold defined by a vector-colouring of a simple $3$-polytope, in particular for a small cover. The proof is based on analysis of results in this direction obtained before by different authors.
