Lagrangian concordance of Legendrian knots
By Baptiste Chantraine. 2006
133 citations recorded by the source corpus.
In this article, we define the notion of a Lagrangian concordance between two Legendrian knots analogous to smooth concordance in the Legendrian context. We show that Legendrian isotopic Legendrian knots are Lagrangian concordant. The focus is primarily on the algebraic aspects of the problem. We study the behavior of the classical invariants (namely the Thurston–Bennequin number and the rotation number) under this relation, and provide some examples of nontrivial Legendrian knots bounding Lagrangian surfaces in D 4. 57R17; 57M50
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ce5e6b21ba187e5a13598484f4bdb5463d5fde76
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In Applied Mathematics
In Geometry and Topology
- Baptiste Chantraine
- Steven Sivek
- Christopher Cornwell
- Lenhard L. Ng
- Frederick J. Bourgeois III
- T. Ekholm
- Michael C. Sullivan
- John B. Etnyre
In Mathematical Physics
- Baptiste Chantraine
- Steven Sivek
- Lenhard L. Ng
- Christopher Cornwell
- Frederick J. Bourgeois III
- T. Ekholm
- Michael C. Sullivan
- John B. Etnyre
Citations in the corpus
- Obstructions to Lagrangian concordance (2014, background): “Chantraine proved in [9], using the augmentation category of Bourgeois–Chantraine [4], that there is a Lagrangian slice knot Λ of type 946 (the mirror of 946) such that Λ 6≺ U .”
- Lagrangian cobordisms via generating families: Construction and geography (2014, unknown): “The fact that Legendrian isotopy induces a Lagrangian cobordism (though without the gf-compatibility) has previously appeared in work of Chantraine [9] and Eliashberg and Gromov [20, Lemma 4.2.5].”
- Bilinearised Legendrian contact homology and the augmentation category (2012, methodology): “We recall the definition of Lagrangian filling which is a special case of Lagrangian cobordism as in [4].”