We prove the equation w.dg A = w.db A for every nuclear Fréchet–Arens–Michael algebra A of finite weak bidimension, where w.dg A is the weak global dimension and w.db A is the weak bidimension of A. Assuming that A has a projective bimodule resolution of finite type, we establish the estimate dg A ≤ db A + 1, where dg A is the global dimension and db A is the bidimension of A. We also prove that dg A = db A = w.dg A = w.db A = n for all nuclear Fréchet –Arens–Michael algebras satisfying the Van den Bergh conditions VdB(n). As an application, we calculate the homological dimensions of the smooth and complex-analytic quantum tori.
Rational homology groups of spaces of non-resultant (that is, having only trivial common zeros) systems of homogeneous quadratic polynomial systems in R^3 are calculated
We prove two new local inequalities for divisors on smooth surfaces and consider several applications of these inequalities.
In this paper, we consider orientation-preserving A-diffeomorphisms of orientable surfaces of genus greater than one that contain a one-dimensional, spaciously located perfect attractor. It is shown that the question of the topological classification of the restrictions of diffeomorphisms to such basic sets is reduced to the problem of the topological classification of pseudo-Anosov homeomorphisms with a marked set of saddle singularities. In particular, a proof is given of the topological classification of A-diffeomorphisms of the surfaces under consideration, announced by Yu. A. Zhirov and RV Plykin, whose nonwandering set consists of a one-dimensional spacious attractor and zero-dimensional sources.
This paper is devoted to the development of the phase-integral method as applied to a boundary-value problem modelling the passage from discrete to continuous spectrum in the non- selfadjoint case. Our aim is to study the patterns and features of the asymptotic distribution of eigenvalues of the problem and to describe the topologically distinct types of spectrum configurations in the quasiclassical limit.
We construct two Lefschetz decompositions of the derived category of coherent sheaves on the Grassmannian of k-dimensional subspaces in a vector space of dimension n. Both of them admit a Lefschetz basis consisting of equivariant vector bundles. We prove fullness of the first decomposition and conjecture it for the second one. In the case when n and k are coprime these decompositions coincide and are minimal. In general, we conjecture minimality of the second decomposition.