相关论文: Lagrangians for the Gopakumar-Vafa conjecture

We consider a family of closed symplectic manifolds 4-manifolds which we call symplectic bielliptic surfaces and study its Lagrangian cobordism group of weakly-exact Lagrangian G-branes (that is, Lagrangians equipped with a grading, a Pin…

We construct graph selectors for compact exact Lagrangians in the cotangent bundle of an orientable, closed manifold. The construction combines Lagrangian spectral invariants developed by Oh and results by Abouzaid about the Fukaya category…

We study Lagrangian cobordism groups of closed symplectic surfaces of genus $g \geq 2$ whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups…

While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely…

The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working…

Using Legendrian immersions and, in particular, Legendre curves in odd dimensional spheres and anti De Sitter spaces, we provide a method of construction of new examples of Hamiltonian-minimal Lagrangian submanifolds in complex projective…

To every Hermitian vector bundle with connection over a compact Riemannian manifold $M$ one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial metric dependent…

We study Lagrangian cobordisms with the tools provided by Lagrangian quantum homology. In particular, we develop the theory for the setting of Lagrangian cobordisms or Lagrangians with cylindrical ends in a Lefschetz fibration, and put the…

This paper classifies separated bounding pairs for Lagrangian submanifolds that are homologically trivial inside the ambient space, under the assumption that restriction on cohomology from the ambient space to the Lagrangian is surjective.…

Let (M,w) be a compact symplectic manifold, and L a compact, embedded Lagrangian submanifold in M. Fukaya, Oh, Ohta and Ono construct Lagrangian Floer cohomology for such M,L, yielding groups HF^*(L,b;\Lambda) for one Lagrangian or…

We show the smooth version of the nearby Lagrangian conjecture for the 2-dimensional pair of pants and the Hamiltonian version for the cylinder. In other words, for any closed exact Lagrangian submanifold of $T^{*}M$, there is a smooth or…

We give a necessary and sufficient condition for lagrangians in a symplectic vector bundle to be deformed stably into transversal lagrangians. In the case of three lagrangians, we show that the associated Grothendieck group can be…

In this paper we use Floer theory to study topological restrictions on Lagrangian embeddings in closed symplectic manifolds. One of the phenomena arising from our results is ``homological rigidity'' of Lagrangian submanifolds. Namely, in…

We prove that Lagrangian cocores and Lagrangian linking disks of a stopped Weinstein manifold generate the Lagrangian cobordism infinity-category. As a geometric consequence, we see that any brane (after stabilization) admits a Lagrangian…

We explain microscopically why split attractor flows, known to underlie certain stationary BPS solutions of four dimensional N=2 supergravity, are the relevant data to describe wrapped D-branes in Calabi-Yau compactifications of type II…

We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations…

Given a monotone Lagrangian submanifold invariant under a loop of Hamiltonian diffeomorphisms, we compute a piece of the closed-open string map into the Hochschild cohomology of the Lagrangian which captures the homology class of the loop's…

We develop Lagrangian Floer Theory for exact, graded, immersed Lagrangians with clean self-intersection using Seidel's setup. A positivity assumption on the index of the self intersection points is imposed to rule out certain (but not all)…

We show that, up to Lagrangian isotopy, there is a unique Lagrangian torus inside each of the following uniruled symplectic four-manifolds: the symplectic vector space $\mathbb{R}^4$, the projective plane $\mathbb{C}P^2$, and the monotone…

This is an introductory review to localization techniques in supersymmetric two-dimensional gauge theories. In particular we describe how to construct Lagrangians of N=(2,2) theories on curved spaces, and how to compute their partition…