We give an explicit formula for sp2n-basic representatives of the cyclic cohomology of the Weyl algebra HC(A2n). This paper can be seen as cyclic addendum to the paper [6] by Feigin, Felder and Shoikhet, where the analogous Hochschild case was treated. As an application, we prove a generalization of a Theorem of Nest and Tsygan concerning the relation of the Todd class and the cyclic cohomology...

The classical boundary-value problem for positive-definite solutions of the Einstein field equations is studied with an arbitrary cosmological constant, in the case of a compact (S) boundary given a biaxial Bianchi-IX positive-definite three-metric, specified by two radii (a, b). For the simplest, four-ball, topology of the manifold with this boundary, the regular classical solutions are found ...

The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent sheaves. The global category is very degenerate in general. Thus, we introduce a new notion of a semiformal deformation, a replacement in algebraic geometry ...

We consider the T–equivariant cohomology of Bott–Samelson desingularisations of Schubert varieties in the flag manifold of a connected semi–simple complex algebraic group of adjoint type with maximal torus T . We construct a combinatorially pure (in the sense of T. Braden and R. Macpherson) sheaf on the Bruhat graph of the associated Weyl group such that its global sections give the T–equivaria...

We show that solutions of the Seiberg-Witten equations lead to nontrivial estimates for the L2-norm of the Weyl curvature of a compact Riemannian 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics on smooth compact 4-manifolds with a non-zero Seiberg-Witten invariant. These results considerably refine those previously obtained [21] by using...

We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds X of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realized as adelic quotients of quaternion algebras over totally real number fields. In the volume aspect we prove a (“Weyl-type”) saving of vol(X)...

A section of a Riemannian G-manifold M is a closed submanifold Σ which meets each orbit orthogonally. It is shown that the algebra of G-invariant differential forms on M which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on Σ which are invariant with respect to the generalized Weyl group of Σ, un...

We investigate collective modes in three dimensional (3D) gapless multi-Weyl semimetals with anisotropic energy band dispersions (i.e., with a positive integer J). For comparison, we also consider the gapless semimetals with the isotropic band dispersions (i.e. E ~ kJ). We calculate analytically long-wavelength plasma frequencies incorporating interband transitions and chiral properties of carr...