Codimension two PL embeddings of spheres with nonstandard regular neighborhoods

dc.creatorCencelj, M.
dc.creatorRepovš, D.
dc.creatorSkopenkov, A.
dc.date2006-08-27
dc.date.accessioned2026-07-07T09:28:55Z
dc.date.available2026-07-07T09:28:55Z
dc.descriptionFor 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 $π_1(S^{k+1}-S^{k-1})\not\cong\Z$).
dc.identifierhttps://arxiv.org/abs/math/0608653
dc.identifierhttp://arxiv.org/abs/math/0608653
dc.identifierChinese Ann. of Math., Ser. B, 28: 5 (2007), 603-608.
dc.identifierdoi:10.1007/s11401-005-0476-2
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157601
dc.subjectGeometric Topology
dc.subject57M25; 57Q40; 57M05; 57N40
dc.titleCodimension two PL embeddings of spheres with nonstandard regular neighborhoods
dc.typetext

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