scholarly journals Automatic transversality in contact homology II: filtrations and computations

2019 ◽  
Vol 120 (6) ◽  
pp. 853-917
Author(s):  
Jo Nelson
Keyword(s):  
Contact Homology

CYLINDRICAL CONTACT HOMOLOGY OF A DEHN TWIST

2009 ◽  
Vol 20 (12) ◽  
pp. 1479-1525
Author(s):  
MEI-LIN YAU
Keyword(s):  
Dehn Twist ◽  
Open Book ◽  
Contact Homology

We use open book representations of contact 3-manifolds to compute the cylindrical contact homology of a Stein-fillable contact 3-manifold represented by the open book whose monodromy is a positive Dehn twist on a torus with boundary.

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 A complete knot invariant from contact homology

2017 ◽  
Vol 211 (3) ◽  
pp. 1149-1200 ◽  
Author(s):  
Tobias Ekholm ◽  
Lenhard Ng ◽  
Vivek Shende
Keyword(s):  
Contact Homology ◽  
Knot Invariant

scholarly journals Reeb periodic orbits after a bypass attachment

2013 ◽  
Vol 35 (2) ◽  
pp. 615-672
Author(s):  
ANNE VAUGON
Keyword(s):  
Periodic Orbits ◽  
Contact Structure ◽  
Convex Surface ◽  
Three Dimensional ◽  
Contact Manifold ◽  
Contact Structures ◽  
Contact Homology ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Manifold With Boundary

AbstractOn a three-dimensional contact manifold with boundary, a bypass attachment is an elementary change of the contact structure consisting in the attachment of a thickened half-disc with a prescribed contact structure along an arc on the boundary. We give a model bypass attachment in which we describe the periodic orbits of the Reeb vector field created by the bypass attachment in terms of Reeb chords of the attachment arc. As an application, we compute the contact homology of a product neighbourhood of a convex surface after a bypass attachment, and the contact homology of some contact structures on solid tori.

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