Related papers: Contact manifolds with symplectomorphic symplectiz…
In this paper, we determine the Euler characteristics and signatures of the exact symplectic fillings of the contact double, 3-fold or 4-fold cyclic covers of the standard contact 3-sphere branched over certain transverse quasi-positive…
Basic properties of even (odd) supermanifolds endowed with a connection respecting a given symplectic structure are studied. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case.
By a result of Eliashberg, every symplectic filling of a three-dimensional contact connected sum is obtained by performing a boundary connected sum on another symplectic filling. We prove a partial generalization of this result for…
In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic…
We consider compact connected six dimensional symplectic manifolds with Hamiltonian SU(2) or SO(3) actions with cyclic principal stabilizers. We classify such manifolds up to equivariant symplectomorphisms.
By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-K\"ahler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a…
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be…
In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the…
We construct an infinite family of odd-symplectic forms (also known as Hamiltonian structures) on the 3-sphere that do not admit a symplectic cobordism to the standard contact structure on the 3-sphere. This answers in the negative a…
We classify closed, simply connected $n$-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions $2\leq n\leq 6$. In dimensions $3k$, $k=1,2$ there is only one such manifold…
We mostly determine which closed smooth oriented 4-manifolds fibering over lower dimensional manifolds are virtually symplectic, i.e. finitely covered by symplectic 4-manifolds.
We demonstrate that the functorial properties of the symplectic field theory under strong cobordisms and surgery cobordisms can produce finite algebraic (planar) torsions from simple examples, which gives a unified treatment of most of the…
If $\eta$ is a contact form on a manifold $M$ such that the orbits of the Reeb vector field form a simple foliation $\mathcal{F}$ on $M$, then the presymplectic 2-form $d\eta$ on $M$ induces a symplectic structure $\omega$ on the quotient…
In this paper, we prove that on any contact manifold, there exists an arbitrary C^{\infty}-small contactomorphism which does not admit a square root. In particular, there exists an arbitrary C^{\infty}-small contactomorphism which is not…
We study symplectic structures on four-dimensional small covers. Our main result shows that every symplectic four-dimensional small cover is aspherical. We then classify symplectic small covers over products of two polygons, proving that…
This paper expands some of the issues of the paper math.SG/0506449. We introduce a new technique to produce symplectic manifolds, by taking a symplectic non-free action of a finite group on a symplectic manifold and resolving symplectically…
In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for…
Let C be the contact structure naturally induced on the lens space L(p,q) by the standard contact structure on the three--sphere. We obtain a complete classification of the symplectic fillings of (L(p,q),C) up to orientation-preserving…
In this paper we are interested in characterizing the standard contact sphere in terms of dynamically convex contact manifolds which admit a Liouville filling with vanishing symplectic homology. We first observe that if the filling is…
We consider certain type of fiber bundles with odd dimensional compact contact base, exact symplectic fibers, and the structure group contained in the group of exact symplectomorphisms of the fiber. We call such fibrations "contact…