Related papers: Subflexible symplectic manifolds

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections…

By studying the action of the Weyl group of a simple Lie algebra on its root lattice, we construct torsion free subgroups of small and explicitly determined index in a large infinite class of Coxeter groups. One spin-off is the construction…

We consider the only one known class of non-K\"ahler irreducible holomorphic symplectic manifolds, described in the works of D. Guan and the first author. Any such manifold $Q$ of dimension $2n-2$ is obtained as a finite degree $n^2$ cover…

The Mishchenko-Fomenko theorem on noncommutative integrability of Hamiltonian systems on a symplectic manifold is extended to the case of noncompact invariant submanifolds.

We prove that homological stability fails for the moduli space of any simply-connected closed smooth 4-manifold in any degree of homology, unlike what happens in all dimensions $\neq 4$. We detect also the homological discrepancy between…

Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein. This…

The harmonic cohomology of a Donaldson symplectic submanifold and of an Auroux symplectic submanifold are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the…

We construct examples of four dimensional manifolds with Spin$^c$-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures are…

We study invariant manifolds of conformal symplectic dynamical systems on a symplectic manifold (M, $\omega$) of dimension $\ge$4. This class of systems is the 1-dimensional extension of symplectic dynamical systems for which the symplectic…

By extending a result of Kronheimer-Mrowka to the family setting, we prove a gluing formula for the family Seiberg-Witten invariant. This formula allows one to compute the invariant for a smooth family of 4-manifolds by cutting it open…

The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…

We present some methods to construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or non-symplectic cyclic isotropy point sets. All such actions are not compatible with any symplectic form.

An oriented closed connected N-manifold M is inflexible if it does not admit self-maps of unbounded degree. In addition, if all the maps from any other oriented closed connected N-manifold have bounded degree, then M is said to be strongly…

This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical…

We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be non-exact and non-compactly supported, provided one uses the correct local system of…

We show, using standard results in length spectrum rigidity and symplectic homology, that if the unit tangent bundles of two compact surfaces of negative curvature are exact symplectomorphic, then the underlying surfaces are isometric, and…

Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner, the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterized in…

We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and…

The special structures that arise in symplectic topology (particularly Gromov--Witten invariants and quantum homology) place as yet rather poorly understood restrictions on the topological properties of symplectomorphism groups. This…

Consider a holomorphic automorphism which acts hyperbolically on some invariant compact set. Then for every point in the compact set there exists a stable manifold, which is a complex manifold diffeomorphic to real Euclidean space. If the…