相关论文: Computing the Cech cohomology of decomposition spa…
We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space $P(k\rho )$, of lines inside…
We investigate two open questions in a cohomology theory relative to the family of finite subgroups. The problem of whether the F-cohomological dimension is subadditive is reduced to extensions by groups of prime order. We show that every…
We investigate deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates deformation spaces. This cohomology turns out to be zero for many linear free divisors and to be…
We examine the Hochschild cohomology governing graded deformations for finite cyclic groups acting on polynomial rings. We classify the infinitesimal graded deformations of the skew group algebra $S\rtimes G$ for a cyclic group $G$ acting…
We replace a ring with a small $\mathbb C$-linear category $\mathcal{C}$, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the…
We describe a "cellular" approach to the computation of the cohomology of a poset with coefficients in a presheaf. A cellular cochain complex is constructed, described explicitly and shown to compute the cohomology under certain…
We define the Hochschild (co)homology of a ringed space relative to a locally free Lie algebroid. Our definitions mimic those of Swan and Caldararu for an algebraic variety. We show that our (co)homology groups can be computed using…
We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an…
Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…
We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…
We compute Hochschild cohomology of projective hypersurfaces starting from the Gerstenhaber-Schack complex of the (restricted) structure sheaf. We are particularly interested in the second cohomology group and its relation with…
We provide an algorithm that, given a finite set of generators for a subgroup $H$ of a finitely generated free group $F$, determines whether $H$ is echelon or not and, in case of affirmative answer, also computes a basis with respect to…
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…
In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^n\times\mathbb{C}^m$ which is defined by the inequality ${\|\zeta\|}^2<e^{-\mu{\|z\|}^2}$.
This paper is devoted to studying certain topological properties of the maximal ideal space of the measure algebra on the circle group. In particular, we focus on Cech cohomologies of this space. Moreover, we show that the Gelfand space of…
In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is \v{C}ech cohomology. We show in particular that the \v{C}ech cohomology groups of the…
We reinterpret algebraic de Rham cohomology for a possibly singular complex variety X as sheaf cohomology in the site of smooth schemes over X with Voevodsky's h-topology. Our results extend to the algebraic de Rham complex as well. Our…
We "solve" the Freed-Witten anomaly equation, i.e., we find a geometrical classification of the B-field and A-field configurations in the presence of D-branes that are anomaly-free. The mathematical setting being provided by the geometry of…
We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon \Delta_{\operatorname{inert}} \to \Delta$ takes general…