Related papers: Cocycles and positive functionals in higher cohomo…

We construct explicit models of universal $H \mathbb{Z}[J^{-1}]$-acyclic spaces $\mathcal M$, for any subset $J$ of the prime numbers. The corresponding nullification functors provide thus plus construction functors for ordinary homology…

Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fr\'echet space structure of the set of holomorphic functions on the complement $\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\, :\,…

We present an unified construction for algebras and modules homologies and cohomologies, in the case of associative, commuttaive, Lie and Gerstenhaber algebras. We make a distinction between the linear part of the construction of algebras…

We construct a number of new spectral sequences for calculating the cyclic cohomology $HC^*_{dg}(A)$ of a differential graded algebra (dga). With these spectral sequences we prove some results about the low dimensional cyclic cohomology and…

We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do…

We prove that the Gerstenhaber bracket on the Hochschild cohomology of the group algebra of a cyclic group over a field of positive characteristic is not trivial. In this case, we relate the Lie algebra structure on the odd degrees of the…

We compute the local cohomology of vector fields on a manifold. In the smooth case this recovers the diagonal cohomology studied in work of Losik, Guillemin, Fuks and others. In the holomorphic case this cohomology has recently appeared in…

We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as…

We show that the category of simplicial sets is a co-reflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straightening functor. We show that using the co-reflector, one can…

The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and…

Let $g$ be a reductive Lie algebra over a field of characteristic zero. Suppose $g$ acts on a complex of vector spaces $M$ by $i_\lambda$ and $L_\lambda$, which satisfy the identities as contraction and Lie derivative do for smooth…

A cocycle category H(X,Y) is defined for objects X and Y in a model category, and it is shown that the set of morphisms [X,Y] is isomorphic to the set of path components of H(X,Y) provided the ambient model category is right proper and…

We study generalizations for higher codimension cycles of several well-known definitions of the nef cone of divisors on a projective variety. These generalizations fix some of the pathologies exhibited by the classical nef cone of higher…

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…

In this paper we propose unifying the categories of cochain complexes $\text{Ch}(\mathcal{C})$ and modules $\widehat{A}\text{-mod}$ over a repetitive algebra $\widehat{A}$. Motivated by their striking similarities and importance, we…

We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with…

For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…

Let $R$ be a commutative ring with unit. We develop a Hochschild cohomology theory in the category $\mathcal{F}$ of linear functors defined from an essentially small symmetric monoidal category enriched in $R$-Mod, to $R$-Mod. The category…

In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…

We consider associative superalgebra realized on the smooth Grassmann-valued functions with compact supports in R^n. The lower Hochschild cohomologies of this superalgebra are found.