Related papers: Hypercohomologies of truncated twisted holomorphic…

We study sheaves of differential forms and their cohomology in the h-topology. This allows to extend standard results from the case of smooth varieties to the general case. As a first application we explain the case of singularities arising…

This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on applications to ordinary cohomology and to…

We prove that a blowing-up formula for the intersection cohomology of the moduli space of rank 2 Higgs bundles over a curve with trivial determinant holds. As an application, we derive the Poincar\'{e} polynomial of the intersection…

We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…

We develop techniques to investigate relativized hierarchical unambiguous computation. We apply our techniques to generalize known constructs involving relativized unambiguity based complexity classes (UP and \mathcal{UP}) to new constructs…

If A is a bialgebra over a field k and M, N are either left-right Yetter-Drinfel'd modules or left-right Hopf modules over A, we construct deformation cohomologies H^*(M,N) as total cohomologies of certain double complexes Y(M,N) and…

We construct $N$-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ which generalize the usual complex $(N=2)$ of differential forms. Although, for $N\geq 3$, the generalized cohomology of these…

This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…

For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finite-dimensional if and only if its global dimension is…

Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…

This paper provides a rigorous account on the geometry of forms on supermanifolds, with a focus on its algebraic-geometric aspects. First, we introduce the de Rham complex of differential forms and we compute its cohomology. We then discuss…

This is a note to revisit interesting results of H. Esnault, C. Sabbah, M. Saito and J.-D. Yu on the Kontsevich complexes from the viewpoint of mixed twistor D-modules. We explicitly describe the V-filtration of the mixed twistor D-modules…

We establish a blow-up formula for Hodge cohomology of locally free sheaves on smooth proper varieties over an algebraically closed field of positive characteristic. For this, we introduce a notion of relative Hodge sheaves and study their…

We discuss automorphisms and pseudo-automorphisms on blowups of complex projective space with an eye to finding ones with interesting dynamical behavior.

In this paper, we prove that any perfect complex of $D^{\infty}$-modules may be reconstructed from its holomorphic solution complex provided that we keep track of the natural topology of this last complex. This is to be compared with the…

We study the de Rham cohomology and the Hodge to de Rham spectral sequence for supervarieties.

We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} structure on the space of holomorphic loops into a Poisson…

We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…

A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…

We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal…