Related papers: Flexible Lagrangians
Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic…
We construct some examples of special Lagrangian submanifolds and Lagrangian self-similar solutions in almost Calabi-Yau cones over toric Sasaki manifolds. For example, for any integer g>0, we can construct a real 6 dimensional Calabi-Yau…
We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian…
In this paper, we study the Seiberg-Witten equations on the product R x Y, where Y is a compact 3-manifold with boundary. Following the approach of Salamon and Wehrheim in the instanton case, we impose Lagrangian boundary conditions for the…
We study how regularity along a submanifold of a differential or microdifferential system can propagate from a family of submanifolds to another. The first result is that a microdifferential system regular along a lagrangian foliation is…
A geometrization of Schmidt-Legendre transformation of the second order Lagrangians is proposed by building a proper Tulczyjew's triplet. The symplectic relation between Ostrogradsky-Legendre and Schmidt-Legendre transformations is…
The Lagrangian formalism on a arbitrary non-fibrating manifold is considered. The kinematical description of this generic situation is based on the concept of (higher-order) Grassmann manifolds which is the factorization of the regular…
In dimensions congruent to 1 modulo 4, we prove that the cotangent bundle of an exotic sphere which does not bound a parallelisable manifold is not symplectomorphic to the cotangent bundle of the standard sphere. More precisely, we prove…
Here we prove that up to diffeomorphism every compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the two-disk with Stein regular fibers, such that the monodromy of the fibration is a symplectomorphism induced by…
We show that any locally planar tropical curve $\Gamma \subset \mathbb{R}^n$ (with unit edge weights) can be realized as the limit of the rescaled moment map images of a family of special Lagrangian submanifolds in $T^*T^n$ with respect to…
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard…
Given a closed, oriented Lagrangian submanifold $L$ in a Liouville domain $\overline{M}$, one can define a Maurer-Cartan element with respect to a certain $L_\infty$-structure on the string homology…
Some nonlocal and nonpolynomial scalar field models originated from p-adic string theory are considered. Infinite number of spacetime derivatives is governed by the Riemann zeta function through d'Alembertian $\Box$ in its argument.…
Special Legendrian Integral Cycles in $S^5$ are the links of the tangent cones to Special Lagrangian integer multiplicity rectifiable currents in Calabi-Yau 3-folds. We show that such Special Legendrian Cycles are smooth except possibly at…
We make the elementary observation that the Lagrangian submanifolds of $\mathbb{C}^n$, for each $n \ge 3$, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and moreover have infinite relative Gromov width. The…
We begin a study of possibilities of describing hadrons in terms of monolocal fields which transform as proper Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible representations. The…
We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise…
Many interesting spaces --- including all positroid strata and wild character varieties --- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We show that the existence of cluster structures on these…
Let $Z \to Y^{2n+1}$ be the bundle of Legendrian $n$-planes over a contact manifold $Y$. We consider a foliation of $Z$ by canonical lifts of Legendrian submanifolds, called \emph{Legendrian submanifold path geometry}, whose flat model is…
The most general geometrical scenario in which the brane-world program can be implemented is investigated. The basic requirement is that it should be consistent with the confinement of gauge interaction, the existence of quantum states and…