Invariants of Legendrian and transverse knots

2015 ◽  
pp. 215-246
Keyword(s):  
Transverse Knots

scholarly journals Filtrations on the knot contact homology of transverse knots

2012 ◽  
Vol 355 (4) ◽  
pp. 1561-1591 ◽  
Author(s):  
Tobias Ekholm ◽  
John Etnyre ◽  
Lenhard Ng ◽  
Michael Sullivan
Keyword(s):  
Contact Homology ◽  
Transverse Knots

scholarly journals Tight contact structures via admissible transverse surgery

2019 ◽  
Vol 28 (04) ◽  
pp. 1950032 ◽  
Author(s):  
J. Conway
Keyword(s):  
Contact Structure ◽  
Contact Structures ◽  
Legendrian Knots ◽  
Tight Contact ◽  
Transverse Knots ◽  
Structure Formula ◽  
Heegaard Floer

We investigate the line between tight and overtwisted for surgeries on fibered transverse knots in contact 3-manifolds. When the contact structure [Formula: see text] is supported by the fibered knot [Formula: see text], we obtain a characterization of when negative surgeries result in a contact structure with nonvanishing Heegaard Floer contact class. To do this, we leverage information about the contact structure [Formula: see text] supported by the mirror knot [Formula: see text]. We derive several corollaries about the existence of tight contact structures, L-space knots outside [Formula: see text], nonplanar contact structures, and nonplanar Legendrian knots.

scholarly journals Legendrian knots, transverse knots and combinatorial Floer homology

2008 ◽  
Vol 12 (2) ◽  
pp. 941-980 ◽  
Author(s):  
Peter Ozsváth ◽  
Zoltán Szabó ◽  
Dylan P Thurston
Keyword(s):  
Floer Homology ◽  
Legendrian Knots ◽  
Transverse Knots

scholarly journals Sutured Floer homology and invariants of Legendrian and transverse knots

2017 ◽  
Vol 21 (3) ◽  
pp. 1469-1582 ◽  
Author(s):  
John Etnyre ◽  
David Vela-Vick ◽  
Rumen Zarev
Keyword(s):  
Floer Homology ◽  
Transverse Knots

scholarly journals Transverse knots and Khovanov homology

2006 ◽  
Vol 13 (4) ◽  
pp. 571-586 ◽  
Author(s):  
Olga Plamenevskaya
Keyword(s):  
Khovanov Homology ◽  
Transverse Knots

A Bennequin Number Estimate for Transverse Knots

2013 ◽  
pp. 265-280 ◽  
Author(s):  
V.V. Goryunov ◽  
J.W. Hill
Keyword(s):  
Transverse Knots

A CONSTRUCTION OF TRANSVERSELY NON-SIMPLE KNOT TYPES

2012 ◽  
Vol 21 (11) ◽  
pp. 1250108
Author(s):  
HIROSHI MATSUDA
Keyword(s):  
The Self ◽  
Linking Number ◽  
Transverse Knots ◽  
Standard Contact

For n = 1, 2 and 3, we construct a pair of transverse knots T1 and [Formula: see text], in the standard contact 3-sphere, satisfying the following properties: (1) the topological knot type of T1 is the same as that of [Formula: see text], (2) the self-linking number of T1 is equal to that of [Formula: see text], (3) [Formula: see text] is obtained from a transverse knot T2 by n stabilizations, and (4) T1 is not transversely isotopic to [Formula: see text].

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