Singularity Knots of Minimal Surfaces in $\mathbb{R}^4$
| dc.creator | Soret, Marc | |
| dc.creator | Ville, Marina | |
| dc.date | 2007-02-09 | |
| dc.date.accessioned | 2026-07-07T07:45:47Z | |
| dc.date.available | 2026-07-07T07:45:47Z | |
| dc.description | We study knots in $\mathbb{S}^3$ obtained by the intersection of a minimal surface in $\mathbb{R}^4$ with a small 3-sphere centered at a branch point. We construct examples of new minimal knots. In particular we show the existence of non-fibered minimal knots. We show that simple minimal knots are either reversible or fully amphicheiral; this yields an obstruction for a given knot to be an iterated knot of a minimal surface. Properties and invariants of these knots such as the algebraic crossing number of a braid representative and the Alexander polynomial are studied. | |
| dc.identifier | https://arxiv.org/abs/math/0702254 | |
| dc.identifier | http://arxiv.org/abs/math/0702254 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123647 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C42 | |
| dc.title | Singularity Knots of Minimal Surfaces in $\mathbb{R}^4$ | |
| dc.type | text |