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Positive knots and Lagrangian fillability


Authors: Kyle Hayden and Joshua M. Sabloff
Journal: Proc. Amer. Math. Soc. 143 (2015), 1813-1821
MSC (2010): Primary 57R17, 57M25
Published electronically: December 3, 2014
MathSciNet review: 3314092
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Abstract: This paper explores the relationship between the existence of an exact embedded Lagrangian filling for a Legendrian knot in the standard contact $ \mathbb{R}^3$ and the hierarchy of positive, strongly quasi-positive, and quasi-positive knots. On one hand, results of Eliashberg and especially Boileau and Orevkov show that every Legendrian knot with an exact, embedded Lagrangian filling is quasi-positive. On the other hand, we show that if a knot type is positive, then it has a Legendrian representative with an exact embedded Lagrangian filling. Further, we produce examples that show that strong quasi-positivity and fillability are independent conditions.


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Additional Information

Kyle Hayden
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
Email: kyle.hayden@bc.edu

Joshua M. Sabloff
Affiliation: Department of Mathematics, Haverford College, Haverford, Pennsylvania 19041
Email: jsabloff@haverford.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12365-3
Received by editor(s): August 1, 2013
Received by editor(s) in revised form: September 10, 2013
Published electronically: December 3, 2014
Additional Notes: The second author was partially supported by NSF grant DMS-0909273.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.