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2022 The existence of a universal transverse knot
Jesús Rodríguez-Viorato
Algebr. Geom. Topol. 22(5): 2187-2237 (2022). DOI: 10.2140/agt.2022.22.2187

Abstract

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:MS3 branched along K such that ξ is contact isotopic to the lifting of ξstd under φ.

Citation

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Jesús Rodríguez-Viorato. "The existence of a universal transverse knot." Algebr. Geom. Topol. 22 (5) 2187 - 2237, 2022. https://doi.org/10.2140/agt.2022.22.2187

Information

Received: 13 January 2020; Revised: 21 October 2020; Accepted: 4 June 2021; Published: 2022
First available in Project Euclid: 10 November 2022

Digital Object Identifier: 10.2140/agt.2022.22.2187

Subjects:
Primary: 53D10
Secondary: 57M12

Keywords: branch coverings , contact 3–manifolds , open book decomposition

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.22 • No. 5 • 2022
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