相关论文: Moment-angle manifolds and Panov's problem

The degree zero part of the quantum cohomology algebra of a smooth Fano toric symplectic manifold is determined by the superpotential function, W, of its moment polytope. In particular, this algebra is semisimple, i.e. splits as a product…

We use the method of homological quantum reduction to construct a deformation quantization on singular symplectic quotients in the situation, where the coefficients of the moment map define a complete intersection. Several examples are…

We introduce Smale-Vietoris diffeomorphisms that include the classical DE-mappings with Smale solenoids. We describe the correspondence between basic sets of axiom A Smale-Vietoris diffeomorphisms and basic sets of nonsingular axiom A…

We present an expanded expository account of the $K$-moment problem for polynomial algebras over \(\R^d\), with special emphasis on compact basic closed semialgebraic sets. The central question is to characterize those linear functionals on…

Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open…

We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the class of semi-positive manifolds with convex boundary. This…

The Generalised Baker--Schmidt Problem (1970) concerns the $f$-dimensional Hausdorff measure of the set of $\psi$-approximable points on a nondegenerate manifold. There are two variants of this problem, concerning simultaneous and dual…

The cut polytope of a graph $G$ is the convex hull of the indicator vectors of all cuts in $G$ and is closely related to the MaxCut problem. We give the facet-description of cut polytopes of $K_{3,3}$-minor-free graphs and introduce an…

We construct a plethora of Anosov-Katok diffeomorphisms with non-ergodic generic measures and various other mixing and topological properties. We also construct an explicit collection of the set containing the generic points of the system…

This paper is about the moment problem on a finite-dimensional vector space of continuous functions. We investigate the structure of the convex cone of moment functionals (supporting hyperplanes, exposed faces, inner points) and treat…

The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…

A novel geometric interpretation of the solutions of the WDVV equations formerly found by A.P. Veselov is suggested.

Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them.…

For Riemannian metrics of constant positive curvature on a punctured sphere with conic singularities at the punctures and co-axial monodromy of the developing map, possible angles at the singularities are completely described. This…

This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative polynomials. By the technique of homogenization, we give a…

Suppose a link K in a 3-manifold M is in bridge position with respect to two different bridge surfaces P and Q, both of which are c-weakly incompressible in the complement of K. Then either P and Q can be properly isotoped to intersect in a…

A maniplex of rank n is a connected, n-valent, edge-coloured graph that generalises abstract polytopes and maps. If the automorphism group of a maniplex M partitions the vertex-set of M into k distinct orbits, we say that M is a k-orbit…

It is shown that the signature of a manifold with a symplectic circle action having only isolated fixed points, equals the alternating sum of the Novikov numbers corresponding to the cohomology class of the generalized moment map. The same…

We investigate how the Minkowski sum of two polytopes affects their graph and, in particular, their diameter. We show that the diameter of the Minkowski sum is bounded below by the diameter of each summand and above by, roughly, the product…

The purpose of this note is to show that classical cobordism arguments, which go back to the pioneering works of Mandelbaum and Moishezon, provide quick and unified proofs of any knot surgered compact simply-connected 4-manifold X_K…