The manifold smoothing problem
The manifold smoothing problem
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流形平滑问题
DOI：
10.1090/s0002-9904-1961-10588-0
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发表时间：
1961
影响因子：
1.3
通讯作者：
S. S. Cairns
中科院分区：
文献类型：
--
作者：
S. S. Cairns
证明开始与修改的程序由于H。Noguchi [5]给出了E在D上携带Pn_ 1到多面体Q~中的e-合痕，并允许一个横矢量场。用C-（n-1）-球面表示Q~的一个邻域，从而可以借助于莫尔斯方法[4]完成证明.他的特殊内点可以归为N。证明是归纳的，需要在下一个较低的维度上部分假设定理1。
The proof commences with a modification of a procedure due to H. Noguchi [5] yielding an e-isotopy of E carrying P n _ 1 , on D, into a polyhedron Q~, admitting a transverse vector field. A neighborhood of Q~ is fibred by C—(n—1)-spheres, which permits a completion of the proof with the aid of Morse's methods [4]. His exceptional interior point can be relegated to N. The proof is inductive, requiring a partial assumption of Theorem 1 in the next lower dimension.