scholarly journals Smoothly non-isotopic Lagrangian disk fillings of Legendrian knots

2020 ◽  
Author(s):  
Youlin Li ◽  
Motoo Tange
Keyword(s):  
Legendrian Knots

scholarly journals Legendrian contact homology and topological entropy

2019 ◽  
Vol 11 (01) ◽  
pp. 53-108 ◽  
Author(s):  
Marcelo R. R. Alves
Keyword(s):  
Growth Rate ◽  
Topological Entropy ◽  
Infinite Family ◽  
Contact Structures ◽  
Legendrian Knots ◽  
Contact Homology ◽  
Contact Manifolds ◽  
3 Dimensional ◽  
Reeb Flows ◽  
Legendrian Contact Homology

In this paper we study the growth rate of a version of Legendrian contact homology, which we call strip Legendrian contact homology, in 3-dimensional contact manifolds and its relation to the topological entropy of Reeb flows. We show that: if for a pair of Legendrian knots in a contact 3-manifold [Formula: see text] the strip Legendrian contact homology is defined and has exponential homotopical growth with respect to the action, then every Reeb flow on [Formula: see text] has positive topological entropy. This has the following dynamical consequence: for all Reeb flows (even degenerate ones) on [Formula: see text] the number of hyperbolic periodic orbits grows exponentially with respect to the period. We show that for an infinite family of 3-manifolds, infinitely many different contact structures exist that possess a pair of Legendrian knots for which the strip Legendrian contact homology has exponential growth rate.

scholarly journals Legendrian knots and exact Lagrangian cobordisms

2016 ◽  
Vol 18 (11) ◽  
pp. 2627-2689 ◽  
Author(s):  
Tobias Ekholm ◽  
Ko Honda ◽  
Tamás Kálmán
Keyword(s):  
Legendrian Knots ◽  
Lagrangian Cobordisms

scholarly journals The nonuniqueness of Chekanov polynomials of Legendrian knots

2005 ◽  
Vol 9 (3) ◽  
pp. 1221-1252 ◽  
Author(s):  
Paul Melvin ◽  
Sumana Shrestha
Keyword(s):  
Legendrian Knots

scholarly journals Invariants of Legendrian Knots and Coherent Orientations

2001 ◽  
Vol 1 (2) ◽  
pp. 321-367 ◽  
Author(s):  
John B. Etnyre ◽  
Lenhard L. Ng ◽  
Joshua M. Sabloff
Keyword(s):  
Legendrian Knots
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