Related papers: A Survey on Nambu-Poisson Brackets
We suggest a homotopical description of the Poisson bracket invariants for tuples of closed sets in symplectic manifolds. It implies that these invariants depend only on the union of the sets along with topological data.
We investigate the birational geometry of Deligne-Mumford stacks and define new birational invariants in this context.
We investigate the geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold. Introduce a noncommutative foundations of these structures for a Poisson algebra. Introduce and investigate noncommutative…
We survey some results on toric topology.
We show that there exists a cut-off version of Nambu-Poisson bracket which defines a finite dimensional Lie 3-algebra. The algebra still satisfies the fundamental identity and thus produces N=8 supersymmetric BLG type equation of motion for…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
This paper investigates different Poisson structures that have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. Our aim is to explore the main brackets which have been proposed and to…
This paper is a survey on the theory of knotoids and braidoids. Knotoids are open ended knot diagrams in surfaces and braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids in…
Survey article on the geometry of spherical varieties. Invited survey for Transformation Groups.
We introduce and study the basic notion of polarized Poisson manifolds generalizing the classical case of Poisson manifolds and extend this last notion for the ${k-}$% symplectic stuctures. And also, we show that for any polarized…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…
This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].
Some geometric structures with associated Riemannian metrics have been considered in the book.
We study various properties of polarized vectorial Poisson structures subordinate to polarized k-symplectic manifolds, and also, we study the notion of polarized vectorial Poisson manifold. Some properties and examples are given.
This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient…
We give a detailed overview over known results for (no-)collision of a body with the boundary of its container.
The aim of this paper is to find all algebraic threefolds admitting quasi-regular Poisson structure. There are three types of such varieties: abelian varieties, smooth flat conic bundles over abelian surfaces and quotients of the product of…