相关论文: On some examples in Symplectic Topology

We classify finite-dimensional nilpotent Lie algebras with $2$-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to $SO_2(\mathbb R)$. This enables one to enlarge the class of nilpotent Lie algebras of…

For any compact almost complex manifold $(M,J)$, the last two authors defined two subgroups $H_J^+(M)$, $H_J^-(M)$ of the degree 2 real de Rham cohomology group $H^2(M, \mathbb{R})$ in arXiv:0708.2520. These are the sets of cohomology…

In this paper I construct, using off the shelf components, a compact symplectic manifold with a non-trivial Hamiltonian circle action that admits no Kaehler structure. The non-triviality of the action is guaranteed by the existence of an…

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses…

In previous work by El Kacimi Alaoui-Guasp-Nicolau, a cohomological criterion is given for a Lie $\mathfrak{g}$-foliation on a compact manifold to be rigid among nearby Lie foliations. Our aim is to look for examples of this rigidity…

We study the existence of lattices in almost abelian Lie groups that admit left invariant locally conformal K\"ahler or locally conformal symplectic structures in order to obtain compact solvmanifolds equipped with these geometric…

Mishchenko-Oliveira proved the piecewise smooth cohomology and Lie algebroid cohomology of a Lie algebroid on a combinatorial compact manifold are isomorphic. In this paper, we describe an application of that result locally trivial Lie…

We consider birational projective contractions f:X -> Y from a smooth symplectic variety X over the complex numbers. We first show that exceptional rational curves on X deform in a family of dimension at least 2n-2. Then we show that these…

This survey presents some recent results by the authors and Polterovich on the topological properties of ruled symplectic manifolds. The bundle M \to P \to B that is associated with a ruled manifold has the group of Hamiltonian…

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic…

We show that a compactly generated locally compact group of polynomial growth having no non-trivial compact normal subgroups can be embedded as a co-compact subgroup into a semidirect product of a connected, simply connected, nilpotent Lie…

We consider symplectic singularities in the sense of A. Beauville as examples of Poisson schemes. Using Poisson methods, we prove that a symplectic singularity admits a finite stratification with smooth symplectic strata. We also prove that…

We describe finite-dimensional smooth Lie groups over local fields of positive characteristic which do not admit an analytic Lie group structure compatible with the given topological group structure, and C^n-Lie groups without a compatible…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal K\"ahler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

We show an alternative construction of the first example of a simply-connected compact symplectic non-formal 8-manifold given in arXiv:math/0506449. We also give an alternative proof of its non-formality using higher order Massey products.

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 consider the 3-point blow-up of the manifold $ (S^2 \times S^2, \sigma \oplus \sigma)$ where $\sigma$ is the standard symplectic form which gives area 1 to the sphere $S^2$, and study its group of symplectomorphisms $\rm{Symp} ( S^2…

Using Cohen's classification of symplectic reflection groups, we prove that the parabolic subgroups, that is, stabilizer subgroups, of a finite symplectic reflection group are themselves symplectic reflection groups. This is the symplectic…