论文标题
将歧管分解为与特定折叠图兼容的子曼群
Decompositions of manifolds into submanifolds compatible with specific fold maps
论文作者
论文摘要
我们通过所谓的折叠图呈现了歧管的新的显式分解，以呈现到较低的尺寸空间。折叠地图形成了一类所谓的通用图，自然而然地概括了摩尔斯的功能。 为了了解全球流形的拓扑结构和不同的结构，分解流形很重要，这在歧管的几何形状上呈现了有趣的主题和问题。 Heegaard分裂的概念是$ 3 $维的封闭和连接的歧管的概念提出了一项开创性的研究。通过所谓的Heegaard表面，$ 3 $维的封闭式和连接的歧管总是分解为所谓的$ 3 $尺寸的手柄的两个副本，该副本是一个封闭且连接的表面。 Heegaard拆分被普遍为2010年代的平滑或PL歧管的多个。作为一种理解方式，这些分解是通过莫尔斯函数和编辑为负面的一般普通平滑图来理解的。
We present new explicit decompositions of manifolds via so-called fold maps into lower dimensional spaces. Fold maps form a nice class of so-called generic maps, generalizing Morse functions naturally. To understand the topologies and the differentibale structures of manifolds globally, decomposing manifolds are important and this presents interesting topics and problems on geometry of manifolds. The notion of a Heegaard splitting of a $3$-dimensional closed and connected manifold presents a pioneering study. A $3$-dimensional closed and connected manifold is always decomposed into two copies of a so-called $3$-dimensional handlebody via a so-called Heegaard surface, which is a closed and connected surface. Heegaard splitiings are generalized as multisections of smooth or PL manifolds in the 2010s. As a way of understanding, these decompositions are understood via Morse functions and general generic smooth maps whose codimensions are negative.
