相关论文: A Survey on Nambu-Poisson Brackets
We study the geometry and codes of quartic surfaces with many cusps. We apply Gr\"obner bases to find examples of various configurations of cusps on quartics.
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson…
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.
In this series of papers, we established that $Q^{\gamma_3}_{d=4}(P)$ is a coboundary in 4D (paper II arXiv:2409.12555), and we presented a series of experimental results about the (non)trivialisation of Kontsevich graph flows of…
We classify linear Nambu structures (which are generalized Poisson structures in Hamiltonian dynamics and which give rise to integrable differential forms and singular foliations), then give a linearization for Nambu structures anf…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.
We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.
This is a non-technical survey of a recent theory of valuations on manifolds constructed in math.MG/0503397, math.MG/0503399, math.MG/0509512, math.MG/0511171 and actually a guide to this series of articles. We review also some recent…
We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie algebroids and, by a sort of duality, to affine analogs of…
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
Gauge theory approach to consideration of the Nambu-Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries, is discussed. The approach is generalized to describe the fundamental branes…
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is that quadratic…
We study the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology, with a view to proving a weak version of the geometrization conjecture for such manifolds.
This is a brief account of the approach to superbranes based upon the concept of Partial Breaking of Global Supersymmetry (PBGS).
The standard definition of the Poisson brackets is generalized to the non-equal-time Poisson brackets. Their relationship to the equal-time Poisson brackets, as well as to the equal- and non-equal-time commutators, is discussed.