Related papers: Folded symplectic forms in contact topology

We define the concept of Lefschetz contact pencil and we show the existence of such structures on any contact manifold. The main idea of the proof is a generalization of the Donaldson arguments used in the symplectic case. We will analyze…

In this note we study the systoles of convex hypersurfaces in $\mathbb{R}^{2n}$ invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the…

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…

Motivated by recent developments in proving the Weinstein conjecture we introduce the notion of covering contact connected sum for virtually contact manifolds and construct virtually contact structures on boundaries of subcritical handle…

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…

We define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with…

Symplectic fillings of standard tight contact structures on lens spaces are understood and classified. The situation is different if one considers non-standard tight structures (i.e. those that are virtually overtwisted), for which a…

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are…

We prove that a Weinstein domain symplectically embedded in a closed symplectic manifold always admits symplectic hypersurfaces in its complement, possibly after a deformation. As a consequence, we obtain an obstruction for a closed…

We observe that nonzero Gromov-Witten invariants with marked point constraints in a closed symplectic manifold imply restrictions on the homology classes that can be represented by contact hypersurfaces. As a special case, contact…

We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated…

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin…

We prove that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology; in certain cases, we prove that all flexible fillings are symplectomorphic. As an application,…

We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens…

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.

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…

We define Symplectic cohomology groups for a class of symplectic fibrations with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative…

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of…

We apply ideas from conformal field theory to study symplectic four-manifolds, by using modular functors to "linearise" Lefschetz fibrations. In Chern-Simons theory this leads to the study of parabolic vector bundles of conformal blocks.…

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…