Singularity Knots of Minimal Surfaces in $\mathbb{R}^4$

dc.creatorSoret, Marc
dc.creatorVille, Marina
dc.date2007-02-09
dc.date.accessioned2026-07-07T07:45:47Z
dc.date.available2026-07-07T07:45:47Z
dc.descriptionWe 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.identifierhttps://arxiv.org/abs/math/0702254
dc.identifierhttp://arxiv.org/abs/math/0702254
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123647
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53C42
dc.titleSingularity Knots of Minimal Surfaces in $\mathbb{R}^4$
dc.typetext

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