Normal surfaces in topologically finite 3-manifolds
Normal surfaces in topologically finite 3-manifolds
复制标题
拓扑有限 3 流形中的法面
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Stephan Tillmann
中科院分区：
文献类型：
--
作者：
Stephan Tillmann
Thurston将三角化紧致3-流形中的法向曲面的概念推广到理想三角化的非紧致3-流形中的自旋法向曲面。本文定义了一种边界曲线映射，它把一个旋转法线曲面作为顶点连接曲面的第一同调群的直和的一个元素。利用边界曲线图研究了旋转法线曲面的拓扑结构，并确定了旋转法线曲面四边形坐标下代数方程组的投影解空间的维数。
The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a boundary curve map which takes a spun-normal surface to an element of the direct sum of the first homology groups of the vertex linking surfaces. The boundary curve map is used to study the topology of a spun-normal surface as well as to determine the dimension of the projective solution space of the algebraic equations arising from the quadrilateral coordinates of spun-normal surfaces.