Floer theory for Lagrangian cobordisms
TL;DR: In this paper, intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold is defined, provided that the Chekanov-Eliashberg algebras of the negative ends of the cobordism admit augmentations.
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Abstract: In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the cobordisms admit augmentations. From this theory we derive several long exact sequences relating the Morse homology of an exact Lagrangian cobordism with the bilinearised contact homologies of its ends. These are then used to investigate the topological properties of exact Lagrangian cobordisms.
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Citations
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Floer homology and lagrangian concordance
Baptiste Chantraine,Georgios Dimitroglou Rizell,Paolo Ghiggini,Roman Golovko +3 more
- 02 Jun 2015
TL;DR: In this article, the authors derive constraints on Lagrangian concordances from Legendrian submanifolds of the standard contact sphere admitting exact Lagrangians fillings, and show that such a concordance induces an isomorphism on the level of bilinearised Legendrian contact cohomology.
29
On homological rigidity and flexibility of exact Lagrangian endocobordisms
TL;DR: In this paper, an exact Lagrangian cobordism L ⊂ ℝ × P × τ� from a Legendrian submanifold Λ to itself satisfies Hi(L; 𝔽) = Hi(Λ; and#x 1d53D;) for any field and given that the concatenation of any spin-exact Lagrangians filling of Λ and L is also spin.
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Functorial LCH for immersed Lagrangian cobordisms
Yu Pan,Dan Rutherford +1 more
TL;DR: In this article, the authors extend the functorality of the Legendrian contact homology DG-algebra (DGA) from embedded exact Lagrangian cobordisms, as in \cite{EHK}, to a class of immersed Lagrangians by considering their Legendrian lifts as conical Legendrian cobordism.
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The minimal length of a Lagrangian cobordism between Legendrians
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TL;DR: In this article, a set of real-valued capacities for a Lagrangian submanifold is derived from a filtered version of Legendrian contact homology, which yield lower bounds on the length of the cobordism.
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Families of Legendrians and Lagrangians with unbounded spectral norm
TL;DR: In this paper, the authors explore two natural generalisations of the above geometric setting in which the bound of the spectral norm fails: first, passing to Legendrian isotopies in the contactisation of the unit co-disc bundle, and, second, considering Hamiltonians but after modifying the codisc bundle by attaching a critical Weinstein one-handle.
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References
•Posted Content
Knots and Contact Geometry
John B. Etnyre,Ko Honda +1 more
TL;DR: In this article, the authors classify Legendrian torus knots and figure eight knots in the tight contact structure on the 3-sphere up to Legendrian isotopy, and obtain the classification of transversal Torus knots.
79
A duality exact sequence for legendrian contact homology
TL;DR: In this article, a long exact sequence for Legendrian submanifolds L⊂P×R was established, where P is an exact symplectic manifold, which admits a Hamiltonian isotopy that displaces the projection of L to P off of itself.
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•Book
An Introduction to Compactness Results in Symplectic Field Theory
Casim Abbas
- 09 Jan 2014
TL;DR: The starting point of this theory are compactness results for holomorphic curves established in the last decade as discussed by the authors, and the author presents a systematic introduction providing a lot of background material which is scattered throughout the literature.
68
Legendrian and transverse twist knots
TL;DR: In this article, a complete classification of Legendrian and transverse representatives of twist knots was given, and it was shown that there are at least Ω(n) different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot with crossing number 2n+1.
55
Lifting pseudo-holomorphic polygons to the symplectisation of $P \times \mathbb{R}$ and applications
TL;DR: In this paper, it was shown that Seidel's isomorphism of the linearised Legendrian contact homology induced by an exact Lagrangian filling and the singular homology of the filling can be defined by counting a cylinder over a Legendrian submanifold.
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