The contact homology of Legendrian submanifolds in R2n+1

By T. Ekholm, John B. Etnyre, Michael C. Sullivan. 2005

167 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7d2c2c12c5b5b760268d0ef43cc19244b7b8d7cd

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Legendrian contact homology in $P \times \mathbb{R}$ (2007, methodology): “In [7, 8], analytical foundations for Legendrian contact homology in the case P = R = C equipped with its standard complex structure were established.”
Legendrian Contact Homology in P X R (2005, methodology): “In [7, 8], analytical foundations for Legendrian contact homology in the case P = R = C equipped with its standard complex structure were established.”
Legendrian ambient surgery and Legendrian contact homology (2012, background): “ve construction that, unfortunately, is weaker than Theorem 1.9 in general. There is a version of the Chekanov-Eliashberg algebra of Lwhose coefﬁcients are taken in the group-ring Z2[H1(L)] (see e.g. [EES1]). In [EENS, Section 2.3.3] this construction was reﬁned to a version where the underlying alg”
Morse flow trees and Legendrian contact homology in 1-jet spaces (2005, unknown): “; /, satisfies (6–5) and the fact that the trivialization compensates for the change in weight, see (6–10), allow us to establish the quadratic estimate by repeating the argument in [4].”
$S^1$-equivariant symplectic homology and linearized contact homology (2012, unknown): “ under ideal transversality assumptions that the cobordism map CHlin ∗ (M′) → CHlin ∗ (M) ﬁts into an exact triangle in which the third term is a group of Legendrian contact homology ﬂavor [26, §2.8] [25] built from cyclic words in Reeb chords with endpoints on S. The casek<n(subcritical surgery)”
Sutures and contact homology I (2010, background): “12, the Legendrian contact homology – due to Chekanov [5] and Eliashberg in dimension three, and Ekholm, Etnyre and Sullivan [10] in higher dimensions – of a stabilized Legendrian submanifold always vanishes.”
A Duality Exact Sequence for Legendrian Contact Homology (2008, background): “4See [4, 7] for proofs of Gromov compactness in the present setting.”
Knot contact homology (2011, background): “hism class of LA(Λ) is an invariant of Λ up to Legendrian isotopy; in particular, its homology LH(Λ) is a Legendrian isotopy invariant. (For the notion of stable tame isomorphism in this setting, see [13].) This result is stated and proven in [15] for the homology-commutative quotient, but the proof”
Effect of Legendrian surgery (2009, methodology): “an submanifold Λ ⊂Y. Assuming it is in general position with respect to the Reeb ﬂow of αwe have a discrete set C(Λ) of non-degenerate chords of the Reeb foliation with ends on Λ. One can assign, see [18], an integer grading |c|to each chord c ∈C(Λ). Note that with our assumptions this grading can b”
Framed knot contact homology (2004, background): “Since its introduction by Eliashberg and Hofer [7], Legendrian contact homology has been studied in many papers, including [1, 4, 9, 14].”
Legendrian fronts for affine varieties (2016, background): “These invariants can be extracted from the Legendrian contact differential graded algebra [20, 28] via the generation criterion [1] and the surgery exact sequences [11, 12].”