非标准正则邻域球面的余维2 PL嵌入
Codimension two PL embeddings of spheres with nonstandard regular neighborhoods
摘要：
对于给定的多面体$K\subset M$，符号$R_M(K)$表示$M$中$K$的正则邻域。本文研究了如下问题：找到所有对$(m,k)$，使得如果$K$是紧$k$ -多面体，$M$是PL $m$ -流形，则对于每两个同伦PL嵌入$f,g:K\to M$，有$R_M(fK)\cong R_M(gK)$.我们证明，$R_{S^{k+2}}(S^k)\not\cong S^k\times D^2$为每个$k\ge2$和{ \it一些} PL球$S^k\subset S^{k+2}$（甚至为{ \it任何} PL球$S^k\subset S^{k+2}$有一个孤立的非局部平坦点的奇异性$S^{k-1}\subset S^{k+1}$，使$π_1(S^{k+1}-S^{k-1})\not\cong\Z$）。
英文摘要：
For a given polyhedron $K\subset M$ the notation $R_M(K)$ denotes a regular neighborhood of $K$ in $M$. We study the following problem: find all pairs $(m,k)$ such that if $K$ is a compact $k$-polyhedron and $M$ a PL $m$-manifold, then $R_M(fK)\cong R_M(gK)$, for each two homotopic PL embeddings $f,g:K\to M$. We prove that $R_{S^{k+2}}(S^k)\not\cong S^k\times D^2$ for each $k\ge2$ and {\it some} PL sphere $S^k\subset S^{k+2}$ (even for {\it any} PL sphere $S^k\subset S^{k+2}$ having an isolated non-locally flat point with the singularity $S^{k-1}\subset S^{k+1}$ such that $π_1(S^{k+1}-S^{k-1})\not\cong\Z$).
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