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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123647We 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.Differential GeometryGeometric Topology53C42Singularity Knots of Minimal Surfaces in $\mathbb{R}^4$text