Related papers: Symplectic and K\"ahler structures on $\mathbb CP^…

Let E be the total space of a locally trivial torus bundle over the surface \Sigma_g of genus g>1. Using the Seiberg--Witten theory and spectral sequences we prove that E carries a symplectic structure if and only if the homology class of…

A description of the fundamental degrees of freedom underlying generalized K\"ahler geometry, which separates its holomorphic moduli from its compatible Riemannian metric in a similar way to the K\"ahler case, has been sought since its…

We generalise the notions of scalar-valued holomorphic $p$-contact and $s$-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values…

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…

A hypersymplectic structure on a 4-manifold is a triple of symplectic forms for which any non-zero linear combination is again symplectic. In 2006, Donaldson conjectured that on a compact 4-manifold any hypersymplectic structure can be…

We study weak versus strong symplectic fillability of some tight contact structures on torus bundles over the circle. In particular, we prove that almost all of these tight contact structures are weakly, but not strongly symplectically…

In a recent preprint Yael Karshon showed that there exist non-conjugate tori in a group of symplectomorphisms of a Hirzebruch surface. She counted them in terms of the cohomology class of the symplectic structure. We show that a similar…

We study harmonic bundles with an additional structure called symplectic structure. We study them for the case of the base manifold is compact and non-compact. For the compact case, we show that a harmonic bundle with a symplectic structure…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…

We recall the fat-graph description of Riemann surfaces $\Sigma_{g,s,n}$ and the corresponding Teichm\"uller spaces $\mathfrak T_{g,s,n}$ with $s>0$ holes and $n>0$ bordered cusps in the hyperbolic geometry setting. If $n>0$, we have a…

Let X be a four-manifold with boundary three manifold M. We shall describe (i) a pre-symplectic structure on the space of connections of the trivial SU(n)-bundle over X that comes from the canonical symplectic structure on the cotangent…

This paper presents two existence h-principles, the first for conformal symplectic structures on closed manifolds, and the second for leafwise conformal symplectic structures on foliated manifolds with non empty boundary. The latter…

Consider a symplectic embedding of a disjoint union of domains into a symplectic manifold $M$. Such an embedding is called Kahler-type, or respectively tame, if it is holomorphic with respect to some (not a priori fixed, Kahler-type)…

Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.…

For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translation G-orbit is a totally real submanifold is induced from a…

We complete the classification of symplectic fillings of tight contact structures on lens spaces. In particular, we show that any symplectic filling $X$ of a virtually overtwisted contact structure on $L(p,q)$ has another symplectic…

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many…

We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.

We give a method to lift $(2,0)$-tensors fields on a manifold $M$ to build symplectic forms on $TM$. Conversely, we show that any symplectic form $\Om$ on $TM$ is symplectomorphic, in a neighborhood of the zero section, to a symplectic form…

Symplectic torus bundles $\xi:T^{2}\to E\to B$ are classified by the second cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a compact, orientable surface, the main theorem of this paper gives a necessary and…