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Archiv der Mathematik

, 97:391 | Cite as

Neighbourhoods and isotopies of knots in contact 3-manifolds

  • Fan Ding
  • Hansjörg Geiges
Article
  • 61 Downloads

Abstract

We prove a neighbourhood theorem for arbitrary knots in contact 3-manifolds. As an application we show that two topologically isotopic Legendrian knots in a contact 3-manifold become Legendrian isotopic after suitable stabilisations.

Mathematics Subject Classification (2010)

53D10 57M25 57R52 

Keywords

Legendrian knot Legendrian stabilisation Contact manifold Isotopy 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of MathematicsPeking UniversityBeijingPeople’s Republic of China
  2. 2.Mathematisches InstitutUniversität zu KölnCologneGermany

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