论文标题
$ z $面向表面的三角形
$Z$-oriented triangulations of surfaces
论文作者
论文摘要
纸张的主要对象是$ z $面向连接的封闭$ 2 $维表面的三角形。地图的$ z $取向是曲折的最小集合，它覆盖了一组边缘。我们有两种可能的边缘可能性 - $ z $ - 方向的锯齿形，沿不同的方向（类型I）或同一方向（II型）通过此边缘。然后，三角剖分中有两种类型的面：第一种类型是当面部的两个边缘为I型时，一个边缘是II型，第二种是当脸部所有边缘均为II型时。我们研究了第一种类型的所有面孔的面向$ z $的三角剖分（在一般情况下，任何$ z $面向的三角剖分都可以切成$ z $面向这种类型的三角剖分）。如果锯齿形在II型的任何边缘之后，锯齿形均具有同一的两个边缘。我们给出了曲折的均匀性的拓扑表征。特别是，我们描述了带有同质曲折的面向$ z $的三角形之间的一对一对应关系，并在表面上封闭了$ 2 $ cell嵌入的$ 2 $ cell嵌入。最后，我们向一种$ z $ - 单模型的一种申请。
The main objects of the paper are $z$-oriented triangulations of connected closed $2$-dimensional surfaces. A $z$-orientation of a map is a minimal collection of zigzags which double covers the set of edges. We have two possibilities for an edge -- zigzags from the $z$-orientation pass through this edge in different directions (type I) or in the same direction (type II). Then there are two types of faces in a triangulation: the first type is when two edges of the face are of type I and one edge is of type II and the second type is when all edges of the face are of type II. We investigate $z$-oriented triangulations with all faces of the first type (in the general case, any $z$-oriented triangulation can be shredded to a $z$-oriented triangulation of such type). A zigzag is homogeneous if it contains precisely two edges of type I after any edge of type II. We give a topological characterization of the homogeneity of zigzags; in particular, we describe a one-to-one correspondence between $z$-oriented triangulations with homogeneous zigzags and closed $2$-cell embeddings of directed Eulerian graphs in surfaces. At the end, we give an application to one type of the $z$-monodromy.
