Computing Homology Invariants of Legendrian Knots

@article{Casey2014ComputingHI,
  title={Computing Homology Invariants of Legendrian Knots},
  author={Emily E. Casey and M. Henry},
  journal={arXiv: Symplectic Geometry},
  year={2014}
}
The Chekanov-Eliashberg differential graded algebra of a Legendrian knot L is a rich source of Legendrian knot invariants, as is the theory of generating families. The set P(L) of homology groups of augmentations of the Chekanov-Eliashberg algebra is an invariant, as is a count of objects from the theory of generating families called graded normal rulings. This article gives two results demonstrating the usefulness of computing the homology group of an augmentation using a combinatorial… 
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References

SHOWING 1-10 OF 22 REFERENCES
Connections between Floer-type invariants and Morse-type invariants of Legendrian knots
We define an algebraic/combinatorial object on the front projection $\Sigma$ of a Legendrian knot called a Morse complex sequence, abbreviated MCS. This object is motivated by the theory of
A COMBINATORIAL DGA FOR LEGENDRIAN KNOTS FROM GENERATING FAMILIES
For a Legendrian knot L ⊂ ℝ3, with a chosen Morse complex sequence (MCS), we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The
The nonuniqueness of Chekanov polynomials of Legendrian knots
Examples are given of prime Legendrian knots in the standard contact 3-space that have arbitrarily many distinct Chekanov polynomials, refuting a conjecture of Lenny Ng. These are constructed using a
Generating family invariants for Legendrian links of unknots
Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R 3 . It is shown that the unknot with maximal Thurston‐Bennequin invariant of 1 has a unique
Augmentations and rulings of Legendrian knots
A connection between holomorphic and generating family invariants of Legendrian knots is established; namely, that the existence of a ruling (or decomposition) of a Legendrian knot is equivalent to
Invariants of Legendrian Knots and Decompositions of Front Diagrams
The authors prove that the sufficient condition for the existence of an augmentation of the Chekanov–Eliashberg differential algebra of a Legendrian knot, which is contained in a recent work of the
Combinatorics of fronts of Legendrian links and the Arnol'd 4-conjectures
Each convex smooth curve on the plane has at least four points at which the curvature of the curve has local extrema. If the curve is generic, then it has an equidistant curve with at least four
Generating function polynomials for legendrian links
It is shown that, in the 1{jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component
The Thurston-Bennequin number, Kauffman polynomial, and ruling invariants of a Legendrian link: The Fuchs conjecture and beyond
Author(s): Rutherford, Dan | Abstract: We show that the ungraded ruling invariants of a Legendrian link can be realized as certain coefficients of the Kauffman polynomial which are non-vanishing if
Computable Legendrian invariants
Abstract We establish tools to facilitate the computation and application of the Chekanov–Eliashberg differential graded algebra (DGA), a Legendrian-isotopy invariant of Legendrian knots and links in
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