Codimension two PL embeddings of spheres with nonstandard regular neighborhoods
| dc.creator | Cencelj, M. | |
| dc.creator | Repovš, D. | |
| dc.creator | Skopenkov, A. | |
| dc.date | 2006-08-27 | |
| dc.date.accessioned | 2026-07-07T09:28:55Z | |
| dc.date.available | 2026-07-07T09:28:55Z | |
| dc.description | 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 $π_1(S^{k+1}-S^{k-1})\not\cong\Z$). | |
| dc.identifier | https://arxiv.org/abs/math/0608653 | |
| dc.identifier | http://arxiv.org/abs/math/0608653 | |
| dc.identifier | Chinese Ann. of Math., Ser. B, 28: 5 (2007), 603-608. | |
| dc.identifier | doi:10.1007/s11401-005-0476-2 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157601 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25; 57Q40; 57M05; 57N40 | |
| dc.title | Codimension two PL embeddings of spheres with nonstandard regular neighborhoods | |
| dc.type | text |