English

Efficient Detection of Borromean Linking in Ellipses

Geometric Topology 2025-09-19 v1

Abstract

We describe a method by which the number of intersections one ellipse makes inside the plane of another can be determined. The method is based on applying a transformation that reverts one ellipse to the unit circle, and examining the intersection points of the transformed second ellipse with the unit circle. This may be used to efficiently determine Hopf linking between two ellipses, or Borromean linking between three ellipses.

Keywords

Cite

@article{arxiv.2509.15104,
  title  = {Efficient Detection of Borromean Linking in Ellipses},
  author = {Jonathan Strange and Ryan Blair and Alexander R. Klotz},
  journal= {arXiv preprint arXiv:2509.15104},
  year   = {2025}
}

Comments

17 pages, 9 figures

R2 v1 2026-07-01T05:44:14.471Z