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The existence of a universal transverse knot

Jesús Rodríguez-Viorato

Algebraic & Geometric Topology 22 (2022) 2187–2237

We prove that there is a knot K transverse to ξstd , the tight contact structure of S3, such that every contact 3–manifold (M,ξ) can be obtained as a contact covering branched along K. By contact covering, we mean a map φ: M S3 branched along K such that ξ is contact isotopic to the lifting of ξstd under φ.

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contact 3–manifolds, branch coverings, open book decomposition
Mathematical Subject Classification 2010
Primary: 53D10
Secondary: 57M12
Received: 13 January 2020
Revised: 21 October 2020
Accepted: 4 June 2021
Published: 25 October 2022
Jesús Rodríguez-Viorato
Centro de Investigación en Matemáticas