Related papers: A note on exact Lagrangian cobordisms with disconn…
We show that up to stabilizations, smooth ribbon cobordisms can be realized by decomposable Lagrangian cobordisms. We also define the notion of stabilization for Lagrangian cobordisms and show that it can be used to find new Lagrangian…
We prove an existence result for exact lagrangian cobordisms between closed legendrians.
We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair $(X,L)$ consisting of an exact symplectic manifold $X$ and an exact…
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…
In the symplectization of standard contact $3$-space, $\mathbb R \times \mathbb R^3$, it is known that an orientable Lagrangian cobordism between a Legendrian knot and itself, also known as an orientable Lagrangian endocobordism for the…
For an embedded exact Lagrangian cobordism between Legendrian submanifolds in the 1-jet bundle, we prove that a generating family linear at infinity on the Legendrian at the negative end extends to a generating family linear at infinity on…
We show that an exact Lagrangian cobordism $L\subset \mathbb R \times P \times \mathbb R$ from a Legendrian submanifold $\Lambda\subset P\times \mathbb R$ to itself satisfies $H_i(L;\mathbb F)=H_i(\Lambda;\mathbb F)$ for any field $\mathbb…
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced from isotopy, spinning, and handle attachment constructions that employ the technique of generating families. Moreover, any Legendrian with a generating family has…
We show that under some topological assumptions, an exact Lagrangian cobordism $(W; L_{0}, L_{1})$ of dimension $dim(W) >5$ is a Lagrangian pseudo-isotopy. This result is a weaker form of a conjecture proposed by Biran and Cornea, which…
We show that if Q is simply connected, every exact Lagrangian cobordism between compact, exact Lagrangians in the cotangent bundle of Q is an h-cobordism. The result is an exercise in basic algebraic topology once one invokes the…
This paper discusses the cobordism of Lagrangian submanifolds (in the monotone setting) and structures it as a category that is related in a functorial way to an appropriate (derived) Fukaya category. Are also discussed obstructions to…
Given an immersed, Maslov-$0$, exact Lagrangian filling of a Legendrian knot, if the filling has a vanishing index and action double point, then through Lagrangian surgery it is possible to obtain a new immersed, Maslov-$0$, exact…
Lagrangian cobordism induces a preorder on the set of Legendrian links in any contact 3-manifold. We show that any finite collection of null-homologous Legendrian links in a tight contact 3-manifold with a common rotation number has an…
We define an invariant of Legendrian links in the double-point enhanced grid homology of a link, and prove that it obstructs decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on $\mathbb R^3$.
We define the notion of special Lagrangian curvature, showing how it may be interpreted as an alternative higher dimensional generalisation of two dimensional Gaussian curvature. We obtain first a local rigidity result for this curvature…
Biran and Cornea showed that monotone Lagrangian cobordisms give an equivalence of objects in the Fukaya category. However, there are currently no known non-trivial examples of monotone Lagrangian cobordisms with two ends. We look at an…
We study the relation of an embedded Lagrangian cobordism between two closed, orientable Legendrian submanifolds of R^{2n+1}. More precisely, we investigate the behavior of the Thurston-Bennequin number and (linearized) Legendrian contact…
We establish an $h$-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact…
In this note we provide explicit constructions of exact Lagrangian embeddings of tori and Klein bottles inside the symplectisation of an overtwisted contact three-manifold. Note that any closed exact Lagrangian in the symplectisation is…
We provide some constructions using Lagrangian cobordisms which improve known examples for some symplectic squeezing problems. Additionally, we prove a flexibility result that Lagrangian submanifolds which are Lagrangian isotopic are also…