论文标题
路径三角剖分，周期和平面细胞复合物上的良好盖。 J.H.C.的扩展Whitehead的同质系统几何实现和E.C. Zeeman的可折叠锥定理
Path Triangulation, Cycles and Good Covers on Planar Cell Complexes. Extension of J.H.C. Whitehead's Homotopy System Geometric Realization and E.C. Zeeman's Collapsible Cone Theorems
论文作者
论文摘要
本文在一个有界的，简单地连接的表面区域中介绍了点的路径三角剖分，从同义理论中用路径三角形代替了Delaunay三角剖分中的普通三角形。 {\ bf路径三角形}的边框是路径$ h：i \ to x，i = [0,1] $的序列。本文的主要结果是（1）圆锥$ d \ times i $折叠到三角形$ h \ bigtriangleup k $，延伸了E.C. Zeeman的dunce hat Cone锥定理，（2）普通的路径三角形的三角形三角形的三角形，一条带有地貌的圆锥形的经验，the triand cmilliar tiles tiles the $ tile $ bill $ bill $ bill $ kill $ kill $ kill $ kill $ kill $ a三角形在几何形式上是带有曲线边缘的三角形的三角形，（4）根据有限细胞复合物的路径三角剖分的自由组呈现定义的几何实现的同型系统扩展了J.H.C. Whitehead的同质系统几何实现定理和（5）细胞复合物的每个路径三角剖分都是良好的覆盖率。
This paper introduces path triangulation of points in a bounded, simply connected surface region, replacing ordinary triangles in a Delaunay triangulation with path triangles from homotopy theory. A {\bf path triangle} has a border that is a sequence of paths $h:I\to X, I=[0,1]$. The main results in this paper are that (1) a cone $D\times I$ collapses to a path triangle $h\bigtriangleup K$, extending E.C. Zeeman's collapsible dunce hat cone theorem, (2) an ordinary path triangle with geometrically realized straight edges generalizes Veech's billiard triangle, (3) a billiard ball $K\times I$ collapses to a round path triangle geometrically realized as a triangle with curviliear edges, (4) a geometrically realized homotopy system defined in terms of free group presentations of path triangulations of finite cell complexes extends J.H.C. Whitehead's homotopy system geometric realization theorem and (5) every path triangulation of a cell complex is a good cover.
