Related papers: Enumerative vs. Symplectic Invariants and Obstruct…
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…
We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.
In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…
After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We…
We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or…
We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $\Omega^2 S^2$…
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
We define a class of symplectic fibrations called symplectic configurations. They are natural generalization of Hamiltonian fibrations. Their geometric and topological properties are investigated. We are mainly concentrated on integral…
We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
Every oriented 4-manifold admits a folded symplectic structure, which in turn determines a homotopy class of compatible almost complex structures that are discontinuous across the folding hypersurface ("fold") in a controlled fashion. We…
We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, \sigma)$. In the case when the algebra $(A, \sigma)$ is Hermitian, or the complexification $(A_{\mathbb{C}},…
We consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections.…
When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers…
We obtain a formula for the number of genus one curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface. This enumerative problem is expressed…
We study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We…
This paper is the last in a series of three papers which investigate pseudoholomorphic strips in the symplectisation of a three dimensional closed contact manifold with a mixed boundary condition. We will prove a compactness and an…
The main theorem of this paper is a result of estimated transversality with respect to stratifications of jet spaces in the approximately holomorphic category over an almost-complex manifold. The notion of asymptotic ampleness of complex…
A symplectic structure on the space of nondegenerate and nonparametrized curves in a locally affine manifold is defined. We also consider several interesting spaces of nondegenerate projective curves endowed with Poisson structures. This…
The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is…