Related papers: Fedosov supermanifolds: II. Normal coordinates

We provide a closed, simply connected, symplectic $6$-manifold having infinitely many codimension $2$ symplectic submanifolds. These are mutually homologous but homotopy inequivalent, and furthermore, they cannot admit complex structures.…

Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but…

We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…

In recent years, $b$-symplectic manifolds have become important structures in the study of symplectic geometry, serving as Poisson manifolds that retain symplectic properties away from a hypersurface. Inspired by this rich landscape,…

We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also…

We introduce a method to resolve a symplectic orbifold into a smooth symplectic manifold. Then we study how the formality and the Lefschetz property of the symplectic resolution are compared with that of the symplectic orbifold. We also…

We overview our recent work defining and studying normal crossings varieties and subvarieties in symplectic topology. This work answers a question of Gromov on the feasibility of introducing singular (sub)varieties into symplectic topology…

We consider a compact complex manifold with smooth Levi convex boundary and a tame symplectic form. Consider a real two-sphere with elliptic and hyperbolic complex points generically embedded to the boundary of manifold. We prove a result…

Convergence and normal continuity analysis of a bivariate non-stationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically…

This note collects a number of standard statements in Riemannian geometry and in Sobolev-space theory that play a prominent role in analytic approaches to symplectic topology. These include relations between connections and complex…

Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds…

We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establishing an extension of the classical map of smooth functions to…

We consider the problem of quantization of smooth symplectic varieties in the algebro-geometric setting. We show that, under appropriate cohomological assumptions, the Fedosov quantization procedure goes through with minimal changes. The…

Relations between the symplectically harmonic cohomology and the coeffective cohomology of a symplectic manifold are obtained. This is achieved through a generalization of the latter, which in addition allows us to provide a coeffective…

The Fedosov deformation quantization on a cotangent bundle with a symplectic connection induced by some linear symmetric connection on the base space is considered. A global construction of the symplectic homogeneous connection on the…

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold $\mathcal M$ is presented as a…

We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [2]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie…

A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular we prove that, under some natural assumption, any…