Singularity Knots of Minimal Surfaces in $\mathbb{R}^4$
Differential Geometry
2007-05-23 v1 Geometric Topology
Abstract
We study knots in obtained by the intersection of a minimal surface in 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.
Cite
@article{arxiv.math/0702254,
title = {Singularity Knots of Minimal Surfaces in $\mathbb{R}^4$},
author = {Marc Soret and Marina Ville},
journal= {arXiv preprint arXiv:math/0702254},
year = {2007}
}