Related papers: Symplectic stability on manifolds with cylindrical…

We prove that the non-squeezing theorem of Gromov holds for symplectomorphisms on an infinite-dimensional symplectic Hilbert space, under the assumption that the image of the ball is convex. The proof is based on the construction by duality…

In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…

This paper defines a symplectic form on the infinite dimensional Fr\'echet manifold of framed curves of fixed length over a simply connected Riemannian manifold of constant curvature. The paper then considers Hamiltonian systems generated…

We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show…

In this paper we study whether symplectic toric manifolds are symplectically cohomologically rigid. Here we say that symplectic cohomological rigidity holds for some family of symplectic manifolds if the members of that family can be…

We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…

In this article, we initiate a geometric measure theoretic approach to symplectic Hodge theory. In particular, we apply one of the central results in geometric measure theory, the Federer-Fleming deformation theorem, together with the…

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact…

Let M be an open, connected manifold. A classical theorem of McDuff and Segal states that the sequence of configuration spaces of n unordered, distinct points in M is homologically stable with coefficients in Z: in each degree, the integral…

This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological…

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673].…

For oriented surfaces $\Sigma$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $\Sigma$ with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a…

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…

We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural symplectic structures are found and described…

We prove a coisotropic intersection result and deduce the following: 1. Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. 2. A stable non-squeezing…

We study the relation between a given set of equations of motion in configuration space and a Poisson bracket. A Poisson structure is consistent with the equations of motion if the symplectic form satisfy some consistency conditions. When…

A stable generalized complex structure is one that is generically symplectic but degenerates along a real codimension two submanifold, where it defines a generalized Calabi-Yau structure. We introduce a Lie algebroid which allows us to view…

Given an embedded stable hypersurface in a four-dimensional symplectic manifold, we prove that it is stable isotopic to a $C^0$-close stable hypersurface with the following property: $C^\infty$-nearby hypersurfaces are generically unstable.…

This paper studies the action of symplectic homeomorphisms on smooth submanifolds, with a main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…