We investigate harmonic forms of geometrically formal metrics, which are defined as those having the exterior product of any two harmonic forms still harmonic. We prove that a formal Sasakian metric can exist only on a real cohomology sphere and that holomorphic forms of a formal Kähler metric are parallel w.r.t. the Levi-Civita connection. In the general Riemannian case a formal metric with ma...

We study the algebraic conditions leading to chain property of complexes for vertex operator algebra [Formula: see text]-point functions (with their convergence assumed) with differential being defined through reduction formulas. The notion cohomology Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings formulas are clarified. A counterpart Bott–Segal theorem in te...

In the work is constructed new acyclic resolutions of quasicoherent sheaves. These resolutions is connected with multidimensional local fields. Then the obtained resolutions is applied for a construction of generalization of the Krichever map to algebraic varieties of any dimension. This map gives in the canonical way two k -subspaces B ⊂ k((z1)) . . . ((zn)) and W ⊂ k((z1)) . . . ((zn)) ⊕r fro...

Let (R,m) be a local ring, I a proper ideal of R and M a finitely generated R-module of dimension d. We discuss the local homology modules of H I (M). When M is Cohen-Macaulay, it is proved that H d m(M) is co-CohenMacaulay of N.dimension d and H x d (H m(M)) = M̂ where x = (x1, . . . , xd) is a system of parameters for M . 2000 Mathematics Subject Classification: 13C14, 13D45

Introduction 2 1. Preliminaries on conformal algebras and modules 4 2. Basic definitions 9 3. Extensions and deformations 13 4. Homology 17 5. Exterior multiplication, contraction, and module structure 18 6. Cohomology of conformal algebras and their annihilation Lie algebras 19 6.1. Cohomology of the basic complex 19 6.2. Cohomology of the reduced complex 21 6.3. Cohomology of conformal algebr...

We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class obtained by differentiating the star-product with respect to the deformation parameter is seen to be closely related to the characteristic class of the quant...

We use bordism theory to construct periodic cohomology theories, which we call elliptic cohomology, for which the cohomology of a point is a ring of modular functions. These are complex-oriented multiplicative cohomology theories, with formal groups associated to the universal elliptic genus studied by a number of authors ([CC, LS, O, W1, Z]). We are unable to find a geometric description for t...

We construct a dGBV algebra from Dolbeault complex of any closed hyperkk ahler manifold. A Frobenius manifold structure on an neighborhood of the origin in Dolbeault cohomology then arises via Manin's generalization of Barannikov-Kontsevich's construction of formal Frobenius manifold structure on formal extended moduli space of a Calabi-Yau manifold. It is explained why these two kinds of forma...