Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
The existence of a universal transverse knot

Jesús Rodríguez-Viorato

Algebraic & Geometric Topology 22 (2022) 2187–2237
Abstract

We prove that there is a knot $K$ transverse to ${\xi }_{\mathrm{std}}$, the tight contact structure of ${S}^{3}$, such that every contact $3$–manifold $\left(M,\xi \right)$ can be obtained as a contact covering branched along $K$. By contact covering, we mean a map $\phi :M\to {S}^{3}$ branched along $K$ such that $\xi$ is contact isotopic to the lifting of ${\xi }_{\mathrm{std}}$ under $\phi$.

Keywords
contact 3–manifolds, branch coverings, open book decomposition
Primary: 53D10
Secondary: 57M12