English

Positive links with arrangements of pseudocircles as shadows

Geometric Topology 2023-12-22 v1 Combinatorics

Abstract

An arrangement of pseudocircles A\mathcal{A} is a collection of Jordan curves in the plane that pairwise intersect (transversally) at exactly two points. How many non-equivalent links have A\mathcal{A} as their shadow? Motivated by this question, we study the number of non-equivalent positive oriented links that have an arrangement of pseudocircles as their shadow. We give sharp estimates on this number when A\mathcal{A} is one of the three unavoidable arrangements of pseudocircles.

Keywords

Cite

@article{arxiv.2312.13808,
  title  = {Positive links with arrangements of pseudocircles as shadows},
  author = {Carolina Medina and Santino Ramirez and Jorge L. Ramirez-Alfonsin and Gelasio Salazar},
  journal= {arXiv preprint arXiv:2312.13808},
  year   = {2023}
}