Bounds for the Thurston-Bennequin number from Floer homology

Abstract

Using a knot concordance invariant from the Heegaard Floer theory of Ozsvath and Szabo, we obtain new bounds for the Thurston-Bennequin and rotation numbers of Legendrian knots in S^3. We also apply these bounds to calculate the knot concordance invariant for certain knots.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-20.abs.html

References in corpus (6)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus
• Heegaard Floer homology and alternating knots
• Computations of the Ozsvath-Szabo knot concordance invariant
• Heegaard Floer homologies and contact structures
• Heegaard Floer Invariants and Tight Contact Three--Manifolds

Cited by in corpus (45)

• Legendrian knots, transverse knots and combinatorial Floer homology
• Computations of the Ozsvath-Szabo knot concordance invariant
• On arc index and maximal Thurston-Bennequin number
• Knot concordance and homology cobordism
• A Legendrian Thurston-Bennequin bound from Khovanov homology
• Ozsvath-Szabo and Rasmussen invariants of cable knots
• Branched covers of quasipositive links and L-spaces
• Ozsvath-Szabo and Rasmussen invariants of doubled knots
• The concordance invariant tau in link grid homology
• Corks, exotic 4-manifolds and knot concordance
• Transverse invariants and right-veering
• Bennequin type inequalities in lens spaces
• Satellite operators with distinct iterates in smooth concordance
• Shake slice and shake concordant knots
• SU(2)-cyclic surgeries and the pillowcase
• On the equivalence of contact invariants in sutured Floer homology theories
• A concordance invariant from the Floer homology of double branched covers
• The Ozsv{á}th-Szab{ó} and Rasmussen concordance invariants are not equal
• Ozsváth-Szabó invariants of contact surgeries
• Up to topological concordance links are strongly quasipositive
• Contact structures and reducible surgeries
• The Khovanov-Rozansky Cohomology and Bennequin Inequalities
• Topological minimal genus and $L^2$-signatures
• On contact type hypersurfaces in 4-space
• Transverse Knots Distinguished by Knot Floer Homology
• An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology
• The Rasmussen invariant of a homogeneous knot
• Concordance of Bing doubles and boundary genus
• Maximal Thurston-Bennequin number and reducible Legendrian surgery
• Instantons, concordance, and Whitehead doubling
• Transverse knots and Khovanov homology
• Analytic knots, satellites and the 4-ball genus
• 4-dimensional aspects of tight contact 3-manifolds
• Characterization of positive links and the $s$-invariant for links
• On the slice genus of quasipositive knots in indefinite 4-manifolds
• A skein approach to Bennequin type inequalities
• On the Lagrangian fillability of almost positive links
• Linear independence of cables in the knot concordance group
• Contact (+1)-surgeries along Legendrian Two-component Links
• An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold
• A bound for rational Thurston-Bennequin invariants
• Comparing Bennequin-type inequalities
• A criterion for the Legendrian simplicity of the connected sum
• Contact (+1)-surgeries on rational homology 3-spheres
• Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex