Related papers: Packing stability for symplectic $4$-manifolds

Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, homological stability…

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…

We construct a new family {K_n} of simply connected symplectic 4-manifolds with the property c_1^2(K_n)/chi(K_n) -> 9 (as n goes to infinity).

We prove homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules…

We prove that the displacement energy of a stable coisotropic submanifold is bounded away from zero if the ambient symplectic manifold is closed, rational and satisfies a mild topological condition.

In this paper we study whether symplectic toric manifolds are symplectically cohomologically rigid. Here we say that symplectic cohomological rigidity holds for some family of symplectic manifolds if the members of that family can be…

We provide a closed, simply connected, symplectic $6$-manifold having infinitely many codimension $2$ symplectic submanifolds. These are mutually homologous but homotopy inequivalent, and furthermore, they cannot admit complex structures.…

We prove that, for any n, there are simply-connected four-manifolds which admit n-tuples of symplectic forms whose first Chern classes have pairwise different divisibilities in integral cohomology. It follows that the moduli space of…

In this paper we show that every degree 2 homology class of a 2n-dimensional symplectic manifold is represented by an immersed symplectic surface if it has positive symplectic area. Moreover, the symplectic surface can be chosen to be…

We show that minimal symplectic 4--manifolds with $b_2^+ >1$ and with residually finite fundamental groups are irreducible. We also give examples of irreducible orientable four--manifolds with indefinite intersection forms which are not…

We show that for each $n \geq 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty)$. We also show that for any $n\geq 2$ and any Salem number $\lambda$, there is a closed arithmetic hyperbolic…

We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures…

Which smooth compact 4-manifolds admit an Einstein metric with non-negative Einstein constant? A complete answer is provided in the special case of 4-manifolds that also happen to admit either a complex structure or a symplectic structure.

We show that smooth and strongly convex bodies in the symplectic $\mathbb R^{2n}$ for $n>1$ with all characteristics planar, or all outer billiard trajectories planar are affine symplectic images of balls.

We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…

We prove that a closed manifold which admits a symplectic-Lipschitz structure has non-vanishing even-degree cohomology groups with real coefficients. In particular, spheres $S^{2n}, n \geq 2$ do not admit symplectic-Lipschitz structures.

We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new topological proofs of those theorems, using embedded surfaces in the 4-ball and branched double covers. These theorems exhibit smooth codimension-zero embeddings of…

It is known that every compact Stein 4-manifolds can be embedded into a simply connected, minimal, closed, symplectic 4-manifold. By using this property, we discuss a new method of constructing corks. This method generates a large class of…

The main result of this paper states that a symplectic s-cobordism of elliptic 3-manifolds is diffeomorphic to a product (assuming a canonical contact structure on the boundary). Based on this theorem, we conjecture that a smooth…

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of…