New York Journal of Mathematics
Volume 29 (2023), 213-230


Rima Chatterjee

Transverse links, open books, and overtwisted manifolds

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Published: February 12, 2023.
Keywords: Open book decomposition, contact manifold, transverse links, support genus.
Subject [2020]: 57K10, 57K33, 53D10.

We prove that transverse links in any contact manifold (M,ξ) can be realized as a sub-binding of a compatible open book decomposition. We define the support genus of a transverse link and prove that the support genus of a transverse knot is zero if there is an overtwisted disk disjoint from it. Next, we find a relationship between the support genus of a transverse link and its Legendrian approximation.


I would like to thank John Etnyre and Shea Vela-Vick for several enlightening conversations. I would also like to thank the anonymous referee for their helpful suggestions and insightful comments. This research is partially supported by NSF Grant 1907654 and the SFB/TRR 191 "Symplectic Structures in Geometry, Algebra and Dynamics, funded by the Deutsche Forschungsgemeinschaff (Project- ID 281071066-TRR 191)".

Author information

Rima Chatterjee:
Mathematisches Institut
Universitat zu Koln
Weyertal 86-90, 50931 Koln, Germany