On Legendrian embeddings into open book decompositions

Selman Akbulut Michigan State University Mehmet Firat Arikan Middle East Technical University

Symplectic Geometry mathscidoc:1912.43037

Arkiv for Matematik, 57, (2), 227 – 245, 2019
We study Legendrian embeddings of a compact Legendrian submanifold L sitting in a closed contact manifold (M,ξ) whose contact structure is supported by a (contact) open book OB on M. We prove that if OB has Weinstein pages, then there exist a contact structure ξ′ on M, isotopic to ξ and supported by OB, and a contactomorphism f:(M,ξ)→(M,ξ′) such that the image f(L) of any such submanifold can be Legendrian isotoped so that it becomes disjoint from the closure of a page of OB.
contact, convex symplectic, Weinstein, Liouville, Lefschetz fibration, open book
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@inproceedings{selman2019on,
  title={On Legendrian embeddings into open book decompositions},
  author={Selman Akbulut, and Mehmet Firat Arikan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204134824091859593},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={2},
  pages={227 – 245},
  year={2019},
}
Selman Akbulut, and Mehmet Firat Arikan. On Legendrian embeddings into open book decompositions. 2019. Vol. 57. In Arkiv for Matematik. pp.227 – 245. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204134824091859593.
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