Positive links with arrangements of pseudocircles as shadows

Carolina Medina; Santino Ramirez; Jorge L. Ramirez-Alfonsin; Gelasio Salazar

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arXiv · 2312.13808

Positive links with arrangements of pseudocircles as shadows

Carolina Medina·Santino Ramirez·Jorge L. Ramirez-Alfonsin·Gelasio Salazar

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Abstract

An arrangement of pseudocircles $\mathcal{A}$ is a collection of Jordan curves in the plane that pairwise intersect (transversally) at exactly two points. How many non-equivalent links have $\mathcal{A}$ 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 $\mathcal{A}$ is one of the three unavoidable arrangements of pseudocircles.

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Carolina Medina, Santino Ramirez, Jorge L. Ramirez-Alfonsin, Gelasio Salazar. 2023-12-21. Positive links with arrangements of pseudocircles as shadows. https://arxiv.org/abs/2312.13808

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