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October 2019 On Legendrian embeddings into open book decompositions
Selman Akbulut, Mehmet Firat Arikan
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Ark. Mat. 57(2): 227-245 (October 2019). DOI: 10.4310/ARKIV.2019.v57.n2.a1

Abstract

We study Legendrian embeddings of a compact Legendrian submanifold $L$ sitting in a closed contact manifold $(M,\xi)$ whose contact structure is supported by a (contact) open book $\mathcal{OB}$ on $M$. We prove that if $\mathcal{OB}$ has Weinstein pages, then there exist a contact structure $\xi^{\prime}$ on $M$, isotopic to $\xi$ and supported by $\mathcal{OB}$, and a contactomorphism $f : (M, \xi) \to (M, \xi^{\prime})$ 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 $\mathcal{OB}$.

Funding Statement

The first author is partially supported by NSF FRG grant DMS-0905917. The second author is partially supported by NSF FRG grant DMS-1065910, and also by TUBITAK grant 1109B321200181.

Citation

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Selman Akbulut. Mehmet Firat Arikan. "On Legendrian embeddings into open book decompositions." Ark. Mat. 57 (2) 227 - 245, October 2019. https://doi.org/10.4310/ARKIV.2019.v57.n2.a1

Information

Received: 2 April 2018; Revised: 2 February 2019; Published: October 2019
First available in Project Euclid: 16 April 2020

zbMATH: 07114505
MathSciNet: MR4018753
Digital Object Identifier: 10.4310/ARKIV.2019.v57.n2.a1

Subjects:
Primary: 57R65, 58A05, 58D27

Rights: Copyright © 2019 Institut Mittag-Leffler

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Vol.57 • No. 2 • October 2019
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