Related papers: From Hypercomplex to Holomorphic Symplectic Struct…

We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.

Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an \afsempol\ arises as a result of generalization of the notion of an alternating…

Almost-complex and hyper-complex manifolds are considered in this paper from the point of view of complex analysis and potential theory. The idea of holomorphic coordinates on an almost-complex manifold $(M,\mathbf{J}%)$ is suggested by D.…

Building of some isomorphic classes for noncanonical hypercomplex number systems o dimension 2 is described. In general case, such systems with specific constraints to structural constants can be isomorphic to complex, dual or double number…

Using odd symplectic structure constructed over tangent bundle of the symplectic manifold, we construct the simple supergeneralization of an arbitrary Hamiltonian mechanics on it. In the case, if the initial mechanics defines Killing vector…

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

We study totally decomposable symplectic and unitary involutions on central simple algebras of index 2 and on split central simple algebras respectively. We show that for every field extension, these involutions are either anisotropic or…

We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish…

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

Examples of nonformal simply connected symplectic manifolds are constructed.

Integrable hypercomplex structures with Hermitian and Norden metrics on Lie groups of dimension 4 are considered. The corresponding five types of invariant hypercomplex structures with hyper-Hermitian metric, studied by M.L. Barberis, are…

For a monotone symplectic manifold and a smooth anticanonical divisor, there is a formal deformation of the symplectic cohomology of the divisor complement, defined by allowing Floer cylinders to intersect the divisor. We compute this…

In this paper we study symplectic involutions and quadratic pairs that become hyperbolic over the function field of a conic. In particular, we classify them in degree 4 and deduce results on 5 dimensional minimal quadratic forms, thus…

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…

In recent times a great amount of progress has been achieved in symplectic and contact geometry, leading to the development of powerful invariants of 3-manifolds such as Heegaard Floer homology and embedded contact homology. These…

We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that…

We prove that quasi-morphisms and quasi-states on a closed integral symplectic manifold descend under symplectic reduction to symplectic hyperplane sections. Along the way we show that quasi-morphisms that arise from spectral invariants are…

We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fibre bundles over complex manifolds. We apply our results in the case of left-invariant generalized complex structures on…

We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…

We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space $H^2(\Lg,k)$ for certain Lie algebras $\Lg$. Among these Lie algebras are filiform CNLAs of dimension $n\le 14$. It turns…