Related papers: Symplectic embeddings in infinite codimension

In this article, we introduce a class of closed $2n$-dimensional almost K\"{a}hler manifold $X$ which called the special symplectic hyperbolic manifold. Those manifolds include K\"{a}hler hyperbolic manifolds. We study the spaces of…

We study symplectic and projective structures on small covers over products of polygons. We introduce the factor-compatible class for small covers over products of polygons and prove that every factor-compatible small cover admits a smooth…

We study fillings of contact structures supported by planar open books by analyzing positive factorizations of their monodromy. Our method is based on Wendl's theorem on symplectic fillings of planar open books. We prove that every…

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…

The first example of a compact manifold admitting both complex and symplectic structures but not admitting a K\"ahler structure is the renowned Kodaira-Thurston manifold. We review its construction and show that this paradigm is very…

A cohomology class u of a topological space X is atoroidal if its pullback to the torus vanishes for every map from a torus to X. Furthermore, X is atoroidally symplectic if there is an atoroidal cohomology class $u\in H^2(X;F)$ such that…

Given a symplectic 4-manifold $(X,\omega)$ with rational symplectic form, Auroux constructed branched coverings to $(CP^2,\omega_{FS})$. By modifying a previous construction of Lambert-Cole--Meier--Starkston, we prove that the branch locus…

For any nonempty, compact and fiberwise convex set $K$ in $T^*\mathbb{R}^n$, we prove an isomorphism between symplectic homology of $K$ and a certain relative homology of loop spaces of $\mathbb{R}^n$. We also prove a formula which computes…

We produce an infinite family of $2$-complexes that are intrinsically linked when embedded into four dimensions. In particular, we show that any embedding into $\mathbb{R}^4$ of the suspension of a graph containing $K_6$ as a minor contains…

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 article, we present new symplectic 4-manifolds with same integral cohomology as $S^{2}\times S^{2}$. The generalization of this construction is given as well, an infinite family of symplectic 4-manifolds cohomology equivalent to…

We introduce in this paper a field theory on symplectic manifolds that are fibered over a real surface with interior marked points and cylindrical ends. We assign to each such object a morphism between certain tensor products of quantum and…

We describe families of monotone symplectic manifolds constructed via the symplectic cutting procedure of Lerman from the cotangent bundle of manifolds endowed with a free circle action. We also give obstructions to the monotone Lagrangian…

Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive…

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 prove that any weakly symplectically fillable contact manifold is tight. Furthermore we verify the strong Weinstein conjecture for contact manifolds that appear as the concave boundary of a directed symplectic cobordism whose positive…

We extend the ``Extension after Restriction Principle'' for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.

In this note we prove that a positive multiple of each even-dimensional integral homology class of a compact symplectic manifold $(M^{2n}, \omega)$ can be represented as the difference of the fundamental classes of two symplectic…

In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popov's horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We…

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…