Positive knots and Lagrangian fillability
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- by Kyle Hayden and Joshua M. Sabloff PDF
- Proc. Amer. Math. Soc. 143 (2015), 1813-1821 Request permission
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.References
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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
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 1813-1821
- MSC (2010): Primary 57R17, 57M25
- DOI: https://doi.org/10.1090/S0002-9939-2014-12365-3
- MathSciNet review: 3314092