Related papers: Symplectic geography problem in dimension six

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…

For oriented surfaces $\Sigma$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $\Sigma$ with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a…

Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…

We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real…

Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.

The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are…

This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.

We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use…

In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The…

Quantum 3D R-matrix in the classical (i.e. functional) limit gives a symplectic map of dynamical variables. The corresponding 3D evolution model is considered. An auxiliary problem for it is a system of linear equations playing the role of…

We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete positive solution of the open problem in dimension two.…

This paper highlights the similarities between even-dimensional geometry (symplectic) and odd-dimensional geometry (cosymplectic). We study the Lagrangian Grassmannian in the cosymplectic setting. The space of compatible co-complex…

In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional…

We point out that the field equations in 5D, with spatial spherical symmetry, possess an extra symmetry that leaves them invariant. This symmetry corresponds to certain simultaneous interchange of coordinates and metric coefficients. As a…

We present constructions of simply connected symplectic 4-manifolds which have (up to sign) one basic class and which fill up the geographical region between the half-Noether and Noether lines.

We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that they support a right-skew-symmetric product. We also study…

In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…

Some aspects of the multidimensional soliton geometry are considered.

In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those…

An orientation preserving diffeomorphism over a surface embedded in a 4-manifold is called extendable, if this diffeomorphism is a restriction of an orientation preserving diffeomorphism on this 4-manifold. In this paper, we investigate…