Classification of framed links in 3-manifolds
| dc.creator | Cencelj, M. | |
| dc.creator | Repovš, D. | |
| dc.creator | Skopenkov, M. | |
| dc.date | 2007-05-29 | |
| dc.date | 2007-06-12 | |
| dc.date.accessioned | 2026-07-07T09:28:52Z | |
| dc.date.available | 2026-07-07T09:28:52Z | |
| dc.description | We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: {\bf Theorem.} Let $M$ be a connected oriented closed smooth 3-manifold. Let $L_1(M)$ be the set of framed links in $M$ up to a framed cobordism. Let $°:L_1(M)\to H_1(M;\Z)$ be the map taking a framed link to its homology class. Then for each $α\in H_1(M;\Z)$ there is a 1-1 correspondence between the set $°\nolimits^{-1}α$ and the group $\Bbb Z_{2d(α)}$, where $d(α)$ is the divisibility of the projection of $α$ to the free part of $H_1(M;\Bbb Z)$. | |
| dc.description | Some references were added and some minor corrections and comments were made | |
| dc.identifier | https://arxiv.org/abs/0705.4166 | |
| dc.identifier | http://arxiv.org/abs/0705.4166 | |
| dc.identifier | Proc. Indian Acad. Sci. (Math. Sci.) 117:3 (2007), 301-306. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157584 | |
| dc.subject | Geometric Topology | |
| dc.subject | Algebraic Topology | |
| dc.subject | 57M20, 57M25, 57M27,57N10, 57N65, 57R20 | |
| dc.title | Classification of framed links in 3-manifolds | |
| dc.type | text |