Related papers: Symplectic 2-handles and transverse links

This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for…

This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their construction, seem to be quite different, but cannot be…

We obtain several results for (iterated) planar contact manifolds in higher dimensions: (1) Iterated planar contact manifolds are not weakly symplectically semi-fillable. This generalizes a 3-dimensional result of Etnyre to a…

Relations between the symplectically harmonic cohomology and the coeffective cohomology of a symplectic manifold are obtained. This is achieved through a generalization of the latter, which in addition allows us to provide a coeffective…

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…

This paper and its prequel ("Part I") prove a generalization of the usual gluing theorem for two index 1 pseudoholomorphic curves U_+ and U_- in the symplectization of a contact 3-manifold. We assume that for each embedded Reeb orbit gamma,…

The symplectization of an overtwisted contact structure in Euclidean 3--space is shown to be an exotic symplectic structure on Euclidean 4--space. The technique can be extended to produce exotic symplectic structures in higher dimensional…

This paper completely answers the question of when contact (r)-surgery on a Legendrian knot in the standard contact structure on the 3-sphere yields a symplectically fillable contact manifold for r in (0,1]. We also give obstructions for…

For a symplectic manifold $(M,\om)$ with exact symplectic form we construct a 2-cocycle on the group of symplectomorphisms and indicate cases when this cocycle is not trivial.

Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface. We define a 2-form on the space of immersed symplectic surfaces in M, and show that the form is closed and non-degenerate, up to reparametrizations. Then we give…

The main purpose of this paper is to summarize the basic ingredients, illustrated with examples, of a pseudoholomorphic curve theory for symplectic 4-orbifolds. These are extensions of relevant work of Gromov, McDuff and Taubes on…

Examples of nonformal simply connected symplectic manifolds are constructed.

We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result by Bertelson-Meigniez, states that in dimension at least 7…

In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic planes. More precisely, we prove that if a Euclidean ball is symplectically embedded in the…

We construct bypass attachments in higher dimensional contact manifolds that, when attached to a neighborhood of a Weinstein hypersurface, yield a neighborhood of a new Weinstein hypersurface, obtained via local modifications to the…

Given a handle decomposition of a 4-manifold with boundary, and an open book decomposition of the boundary, we show how to produce a trisection diagram of a trisection of the 4-manifold inducing the given open book. We do this by making the…

Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…

Given a smooth, closed, oriented 4-manifold X and alpha in H_2(X,Z) such that alpha.alpha > 0, a closed 2-form w is constructed, Poincare dual to alpha, which is symplectic on the complement of a finite set of unknotted circles. The number…

Exterior differential forms with values in the (Kostant's) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative…

Under the assumption that the X-ray transform over symmetric solenoidal 2-tensors is injective, we prove that smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set are locally…