scholarly journals Duality for Legendrian contact homology

2006 ◽  
Vol 10 (4) ◽  
pp. 2351-2381 ◽  
Author(s):  
Joshua M Sabloff
Keyword(s):  
Contact Homology ◽  
Legendrian Contact Homology

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 contact homology and nondestabilizability

2011 ◽  
Vol 9 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Clayton Shonkwiler ◽  
David Shea Vela-Vick
Keyword(s):  
Contact Homology ◽  
Legendrian Contact Homology

scholarly journals Cellular Legendrian contact homology for surfaces, part II

2019 ◽  
Vol 30 (07) ◽  
pp. 1950036
Author(s):  
Daniel Rutherford ◽  
Michael Sullivan
Keyword(s):  
Explicit Construction ◽  
Jet Spaces ◽  
Contact Homology ◽  
Cellular Computation ◽  
Legendrian Contact Homology

This paper is a continuation of [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)]. For Legendrian surfaces in [Formula: see text]-jet spaces, we prove that the Cellular DGA defined in [Cellular computation of Legendrian contact homology for surfaces, preprint (2016)] is stable tame isomorphic to the Legendrian contact homology DGA, modulo the explicit construction of a specific Legendrian surface. In [Cellular computation of Legendrian contact homology for surfaces, to appear in Internat. J. Math.], we construct this surface, thereby completing Theorem 5.1 and the proof of the isomorphism.

scholarly journals Cellular Legendrian contact homology for surfaces, part I

2020 ◽  
Vol 374 ◽  
pp. 107348
Author(s):  
Dan Rutherford ◽  
Michael Sullivan
Keyword(s):  
Contact Homology ◽  
Legendrian Contact Homology

scholarly journals Legendrian ambient surgery and Legendrian contact homology

2016 ◽  
Vol 14 (3) ◽  
pp. 811-901 ◽  
Author(s):  
Georgios Dimitroglou Rizell
Keyword(s):  
Contact Homology ◽  
Legendrian Contact Homology

Cellular Legendrian contact homology for surfaces, part III

2019 ◽  
Vol 30 (07) ◽  
pp. 1950037
Author(s):  
Daniel Rutherford ◽  
Michael Sullivan
Keyword(s):  
Gradient Flow ◽  
Contact Homology ◽  
Cellular Computation ◽  
Legendrian Submanifolds ◽  
Legendrian Contact Homology ◽  
Differential Geom

This paper is a continuation of [D. Rutherford and M. Sullivan, Cellular computation of Legendrian contact homology for surfaces, Part II, to appear in Internat. J. Math.]. We construct by-hand Legendrian surfaces for which specific properties of their gradient flow trees hold. These properties enable us to complete the proof in [D. Rutherford and M. Sullivan, Cellular computation of Legendrian contact homology for surfaces, Part II, to appear in Internat. J. Math.] that the Cellular DGA defined in [D. Rutherford and M. Sullivan, Cellular computation of Legendrian contact homology for surfaces, Part I, preprint (2016), arXiv:1608.02984] is stable tame isomorphic to the Legendrian contact homology DGA defined in [T. Ekholm, J. Etnyre and M. Sullivan, The contact homology of Legendrian submanifolds in [Formula: see text], J. Differential Geom. 71(2) (2005) 177–305].

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