PL equivariant surgery and invariant decompositions of 3-manifolds
PL equivariant surgery and invariant decompositions of 3-manifolds
复制标题
PL 等变手术和 3 流形的不变分解
DOI：
10.1016/0001-8708(89)90067-4
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发表时间：
1989
影响因子：
1.7
通讯作者：
J.Hyam Rubinstein
中科院分区：
文献类型：
--
作者：
W. Jaco;J.Hyam Rubinstein
利用法向曲面理论[H，， J2]，引入了最小权值法向曲面的概念。法向曲面的权值是该曲面的法向同位素类的非负整数不变量。如果我们关注某一类法线曲面，并选择使该类权值最小的代表，那么我们就得到了权值最小的法线曲面。值得注意的是，这些最小重量的法向曲面显示出许多与最小面积（最小）曲面相同的有用特性。它们提供了一个分段线性（PL）环境，以获得来自最小面积表面的分析和几何的最新拓扑结果。在一系列令人印象深刻的论文中，Meeks和Yau [MY i， MY z, MY 3， MY,， MY,], Meeks， Simon和Yau [MSY]， Scott [S]， Meeks和Scott [MS]， Freedman， Hass和Scott [FHS]将最小面积曲面的分析和几何引入到关于3流形的拓扑问题的研究中。其结果导致了许多突出问题的解决，在3流形的拓扑结构。由于使用这些新技术解决的大多数问题本质上都是拓扑问题，因此人们认为应该采用更拓扑的方法来证明这些结果。此外，大部分工作在理论方面
Using normal surface theory [H,, J2], we introduce the notion of least weight normal surfaces. The weight of a normal surface is a nonnegative integer invariant of the normal isotopy class of the surface. If we focus on a particular class of normal surfaces and choose representatives which minimize the weight over the class, then we have least weight normal surfaces. It is remarkable how these least weight normal surfaces exhibit many of the same useful properties as least area (minimal) surfaces. They provide a piecewise linear (PL) environment to obtain the recent topological results coming from the analysis and geometry of least area surfaces. In an impressive series of papers Meeks and Yau [MY i, MY z, MY 3, MY,, MY,], Meeks, Simon, and Yau [MSY], Scott [S], Meeks and Scott [MS], and Freedman, Hass, and Scott [FHS] introduced the analysis and geometry of least area surfaces into the study of topological questions about 3-manifolds. The consequences have led to the resolution of many outstanding problems in the topology of 3-manifolds. Since most of the problems being solved with these new techniques are topological in nature, it has been felt that there should be a more topological approach to the proofs of these results. Besides, the bulk of the work in the theory of