• Corpus ID: 244462897

Augmented Legendrian cobordism in $J^1S^1$

@inproceedings{Pan2021AugmentedLC,
  title={Augmented Legendrian cobordism in \$J^1S^1\$},
  author={Yu Pan and Dan Rutherford},
  year={2021}
}
We consider Legendrian links and tangles in JS and J[0, 1] equipped with Morse complex families over a field F and classify them up to Legendrian cobordism. When the coefficient field is F2 this provides a cobordism classification for Legendrians equipped with augmentations of the Legendrian contact homology DG-algebras. A complete set of invariants, for which arbitrary values may be obtained, is provided by the fiber cohomology, a graded monodromy matrix, and a mod 2 spin number. We apply the… 
1 Citations

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References

SHOWING 1-10 OF 44 REFERENCES

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

A Legendrian Turaev torsion via generating families

We introduce a Legendrian invariant built out of the Turaev torsion of generating families. This invariant is defined for a certain class of Legendrian submanifolds of 1-jet spaces, which we call of

Generating families and Legendrian contact homology in the standard contact space

We show that if a Legendrian knot in a standard contact space ℝ3 possesses a generating family, then there exists an augmentation of the Chekanov–Eliashberg differential graded algebra so that the

Ruling polynomials and augmentations over finite fields

For any Legendrian link, L , in (R3,ker(dz‐ydx)), we define invariants, Augm(L,q) , as normalized counts of augmentations from the Legendrian contact homology differential graded algebra (DGA) of L

Generalized normal rulings and invariants of Legendrian solid torus links

For Legendrian links in the 1-jet space of $S^1$ we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the notion of normal

Legendrian Contact Homology in P X R

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such

Sheaves via augmentations of Legendrian surfaces

Given an augmentation for a Legendrian surface in a $1$-jet space, $\Lambda \subset J^1(M)$, we explicitly construct an object, $\mathcal{F} \in Sh_{\Lambda}$, of the (derived) category from

Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra

We study satellites of Legendrian knots in R^3 and their relation to the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence

Augmentations are sheaves

We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category