Related papers: Contact Dynamics versus Legendrian and Lagrangian …
Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical field theory. In particular, their…
We obtain a minimal form of the two-derivative three-nucleon contact Lagrangian, by imposing all constraints deriving from discrete symmetries, Fierz identities and Poincare' covariance. The resulting interaction, depending on 13 unknown…
The conormal lift of a link $K$ in $\R^3$ is a Legendrian submanifold $\Lambda_K$ in the unit cotangent bundle $U^* \R^3$ of $\R^3$ with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link…
Let $\Lambda$ be a closed, connected Legendrian submanifold of the 1-jet space of a smooth $n$-dimensional manifold. Associated to $\Lambda$ there is a Legendrian invariant called Legendrian contact homology, which is defined by counting…
We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and to the combinatorial objects as N-graphs. First, we develop…
We introduce the notion of coLegendrian submanifold in a contact manifold as a middle-dimensional coisotropic submanifold and study its existence in dimension $5$ via contact Morse theory. As an application, the second generation of Orange…
We show that there exists a natural Tulczyjew triple in the dynamics of objects for which the standard kinematic configuration space $TM$, i.e. the tangent bundle, is replaced with its $n$-th exterior power, i.e. the bundle of tangent…
We prove, for a class of contact manifolds, that the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and dynamics of contactomorphisms. It gives rise to…
We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both…
We show that a contact $(+1)$-surgery along a Legendrian sphere in a flexibly fillable contact manifold ($c_1=0$ if not subcritical) yields a contact manifold that is algebraically overtwisted if the Legendrian's homology class is not…
Some mechanical systems with dissipation can be described within the framework of the so-called contact mechanics: a modified form of the Euler-Lagrange equations stemming from Herglotz's variational principle, which admits a geometric…
All knots in $R^3$ possess Seifert surfaces, and so the classical Thurston-Bennequin and rotation (or Maslov) invariants for Legendrian knots in a contact structure on $R^3$ can be defined. The definitions extend easily to null-homologous…
The purposes of the present paper are two-fold. Firstly we further develop the interplay between the contact Hamiltonian geometry and the geometric analysis of Hamiltonian-perturbed contact instantons with the Legendrian boundary condition,…
In this paper we construct an $\mathcal{A}_\infty$-category associated to a Legendrian submanifold of jet spaces. Objects of the category are augmentations of the Chekanov algebra $\mathcal{A}(\Lambda)$ and the homology of the morphism…
By introducing an integration factor to the differential one-form of contact dynamics, equations of motion are derived variationally, and contact Poisson bracket and contact Lagrangian are formulated. Discrete symplectic integrator, named…
We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\subset X$ is an exact Lagrangian submanifold of an exact…
We use the Ozsv\'ath-Szab\'o contact invariants to distinguish between tight contact structures obtained by Legendrian surgeries on stabilized Legendrian links in tight contact 3-manifolds. We also discuss the implication of our result on…
An exact Lagrangian submanifold $L$ in the symplectization of standard contact $(2n-1)$-space with Legendrian boundary $\Sigma$ can be glued to itself along $\Sigma$. This gives a Legendrian embedding $\Lambda(L,L)$ of the double of $L$…
Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical…
We introduce topological contact dynamics of a smooth manifold carrying a cooriented contact structure, generalizing previous work in the case of a symplectic structure [MO07] or a contact form [BS12]. A topological contact isotopy is not…