Related papers: Explicit concave fillings of contact three-manifol…
This paper deals with the following question: which manifolds can be realized as leaves of codimension-1 symplectic foliations on closed manifolds? We first observe that leaves of symplectic foliations are necessarily strongly geometrically…
We construct explicit maximal symplectic packings of minimal rational and ruled symplectic 4-manifolds by few balls in a very simple way.
The aim of this paper is to address the following question: given a contact manifold $(\Sigma, \xi)$, what can be said about the aspherical symplectic manifolds $(W, \omega)$ bounded by $(\Sigma, \xi)$ ? We first extend a theorem of…
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure.…
We establish the relationship between folded symplectic forms and convex hypersurface theory in contact topology. As an application, we use convex hypersurface theory to reprove and strengthen the existence result for folded symplectic…
Spinal open book decompositions provide a natural generalization of open book decompositions. We show that any minimal symplectic filling of a contact 3-manifold supported by a planar spinal open book is deformation equivalent to the…
We introduce a streamlined procedure for constructing small symplectic $4$-manifolds via contact gluing, based on a technique invented by David Gay around 2000. We give several applications of this procedure, which produced results…
In a compact, symplectic real manifold, i.e supporting an antisymplectic involution, we use Donaldson's construction to build a codimension 2 symplectic submanifold invariant under the action of the involution. If the real part of the…
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
We construct infinitely many non-diffeomorphic examples of $5$-dimensional contact manifolds which are tight, admit no strong fillings, and do not have Giroux torsion. We obtain obstruction results for symplectic cobordisms, for which we…
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…
We show that certain classes of contact 3-manifolds do not admit non-separating contact type embeddings into any closed symplectic 4-manifolds, e.g. this is the case for all contact manifolds that are (partially) planar or have Giroux…
Let $M$ be a closed 4-manifold with a free circle action. If the orbit manifold $N^3$ satisfies an appropriate fibering condition, then we show how to represent a cone in $H^2(M;\R)$ by symplectic forms. This generalizes earlier…
We show that any closed oriented 3-manifold can be topologically embedded in some simply-connected closed symplectic 4-manifold, and that it can be made a smooth embedding after one stabilization. As a corollary of the proof we show that…
This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $ D $ that can be embedded symplectically into a closed…
According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle…
Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…
We consider a compact complex manifold with smooth Levi convex boundary and a tame symplectic form. Consider a real two-sphere with elliptic and hyperbolic complex points generically embedded to the boundary of manifold. We prove a result…
We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic…
We use spinal open books to construct contact manifolds with infinitely many different Weinstein fillings in any odd dimension $> 1$, which were previously unknown for dimensions equal to $4n+1$. The argument does not involve understanding…