On Legendrian embbeddings into open book decompositions

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Akbulut S., Arikan M. F.

ARKIV FOR MATEMATIK, no.2, pp.227-245, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2019
  • Doi Number: 10.4310/arkiv.2019.v57.n2.a1
  • Journal Name: ARKIV FOR MATEMATIK
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.227-245
  • Middle East Technical University Affiliated: Yes

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 OB on M. We prove that if OB has Weinstein pages, then there exist a contact structure xi' on M, isotopic to xi and supported by OB, and a contactomorphism f:(M, xi) -> (M, xi') 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.