Topologically Trivial Legendrian Knots
By Y. Eliashberg, Maia Fraser. 2008
121 citations recorded by the source corpus.
The paper deals with topologically trivial Legendrian knots in tight and overtwisted contact 3-manifolds. The first part contains a thorough exposition of the proof of the classification of topologically trivial Legendrian knots (i.e. Legendrian knots bounding embedded 2-disks) in tight contact 3-manifolds. This part was essentially written more than 10 years ago, but only a short version, without the detailed proofs, was published (in CRM Proc. Lecture Notes, Vol. 15, 1998). That paper also briefly discussed the overtwisted case. The final part of the present paper contains a more systematic discussion of Legendrian knots in overtwisted contact manifolds, and in particular, gives the coarse classification (i.e. classification up to a global contactomorphism) of topologically trivial Legendrian knots in overtwisted contact S^3.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a8d384b59f7c2aef8e0c58c3d4804f97aa8fa34a
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In Applied Mathematics
In Geometry and Topology
- A. Stipsicz
- P. Lisca
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- J. Greene
- John A. Baldwin
- Kristen Hendricks
In Mathematical Physics
- A. Stipsicz
- P. Lisca
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- John A. Baldwin
- Jacob Rasmussen
- J. Greene
Citations in the corpus
- Legendrian fronts for affine varieties (2016, methodology): “In the 3–dimensional case this can be proven using strictly 3–dimensional different methods [20] since topologically trivial Legendrian unknots are classified [28].”
- Grid Homology for Knots and Links (2015, methodology): “Legendrian simplicity of various knot types (including the unknot [39], torus knots and the figure-eight knot [44, 46]) has been established using cut-andpaste methods in contact topology, relying on convex surface theory [73] and bypasses [90].”
- Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, background): “(For more on knots in overtwisted contact structures, see [5, 6, 8, 16].”