3-manifold

Today , the main means of the study of the 3-manifold are the algebraic method , geometrical method , and combinatorial method .

目前，关于三维流形理论的研究主要有代数方法，几何方法和组合方法。

Nowadays , the 3-manifold theory is the one of the hotspots in the research of the low-dimension topology .

三维流形理论是当前低维拓扑学研究的热点方向之一。

Corresponding to each global tangent frame , we define a Poisson matrix on the 3-manifold .

对于3-流形上任一整体切标架，定义了一个Poisson矩阵，并给出：Poisson矩阵在标架改变时的变化规律。

In this paper , we will consider some problems about the degenerating handle additions in the 3-manifold theory by combinatorial method .

本文主要运用组合的方法来研究三维流形中的一些问题，即双曲流形上退化的把柄添加及与之相关的内容。

In this paper , the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology .

本文利用可定向3-流形切丛的平凡性，在3维几何上建立了一种整体标架法。

In this thesis , our main aim is to estimate the minimal geometrical intersection number of two degenerating slope on hyperbolic 3-manifold , this is also one of the hotspots in the 3-manifold theory .

在本文中，我们将引用几何相交数的概念来估测双曲流形上退化的把柄添加的个数，这也是三维流形理论中比较热点的话题之一。