Related papers: Hamiltonian linking and Symplectic packing

For the 1+1 dimensional Lax pair with a symplectic symmetry and cyclic symmetries, it is shown that there is a natural finite dimensional Hamiltonian system related to it by presenting a unified Lax matrix. The Liouville integrability of…

We give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg-Steenrod axioms except for the dimension axiom. The resulting long exact sequence of a pair…

This is a light survey article about the origins of contact and symplectic topology in dynamics and the more recent developments in the field. In lieu of formulas, numerous anecdotes are given.

We provide an explicit description of symplectic leaves of a simply connected connected semisimple complex Lie group equipped with the standard Poisson-Lie structure. This sharpens previously known descriptions of the symplectic leaves as…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

For a graph $G$ the random $n$-lift of $G$ is obtained by replacing each of its vertices by a set of $n$ vertices, and joining a pair of sets by a random matching whenever the corresponding vertices of $G$ are adjacent. We show that…

We show that any smooth one-dimensional link in the real projective three-plane is the fixed-point locus of a smooth symplectic surface in the complex projective three-plane which is invariant under complex conjugation. The degree of the…

We show that the averaged equation for a one-frequency fast-oscillating Hamiltonian system is the result of symplectic reduction of a certain natural system on the corresponding $S^1$-bundle with respect to the circle action. Furthermore,…

We give examples of symplectic actions of a cyclic group, inducing a trivial action on homology, on four-manifolds that admit Hamiltonian circle actions, and show that they do not extend to Hamiltonian circle actions. Our work applies…

We construct an $L_\infty$-algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to the universal central extension of the Lie algebra of Hamiltonian vector fields.

We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In…

In this article, we treat G_2-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G_2-structure; in…

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…

Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a quantizable, compact, symplectic manifold $(M,\omega)$. We prove the existence of an action integral around loops in $\text{Ham(M)}$, and determine the value of this…

The gauge usually adopted for extracting the reduced Hamiltonian of a thin spherical shell of matter in general relativity, becomes singular when dealing with two or more intersecting shells. We introduce here a more general class of gauges…

We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimally coupled fermion fields to the Holst action. These formulations are achieved by making a suitable parametrization of both the tetrad and the…

We construct infinitely many Legendrian links in the standard contact $\mathbb{R}^3$ with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in $S^3$ that bound topologically distinct pieces…

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…