Related papers: The cohomology algebra of polyhedral product space…
In this paper, we investigate the existence of free involutions on some Wall manifolds and we compute the mod 2 cohomology algebra of the correspondent orbit space.
Let X^{circ} be the space of all labeled tetrahedra in P^{3}. In [BGS] we constructed a smooth symmetric compactification X-tilde of X^{circ}. In this article we show that the complement X-tilde smallsetminus X^{circ} is a divisor with…
The theory of bounded cohomology of groups has many applications. A key open problem is to compute the full bounded cohomology $H_b^n(F, R)$ of a non-abelian free group $F$ with trivial real coefficients. It is known that $H_b^n(F,R)$ is…
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…
Let R\_{0,n} be the Clifford algebra of the antieuclidean vector space of dimension n. The aim is to built a function theory analogous to the one in the C case. In the latter case, the product of two holomorphic functions is holomorphic,…
Let $\Omega$ be a tiling space and let $G$ be the maximal group of rotations which fixes $\Omega$. Then the cohomology of $\Omega$ and $\Omega/G$ are both invariants which give useful geometric information about the tilings in $\Omega$. The…
We show that there is an action of the symmetric group on the Hochschild cochain complex of a twisted group algebra with coefficients in a bimodule. This allows us to define the symmetric Hochschild cohomology of twisted group algebras,…
The moduli stack of representations of a quiver, or coherent sheaves on a proper curve, carries two structures on its cohomology: a Hall algebra and braided vertex coalgebra. We show that they are compatible, by developing a formulation of…
Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which "forces its border." One can then represent the tiling space as an inverse limit of an inflation…
A general method for establishing results over a commutative complete intersection local ring by passing to differential graded modules over a graded exterior algebra is described. It is used to deduce, in a uniform way, results on the…
Let $I=(\mathbb{Z}^3,26,6,B)$ be a 3D digital image, let $Q(I)$ be the associated cubical complex and let $\partial Q(I)$ be the subcomplex of $Q(I)$ whose maximal cells are the quadrangles of $Q(I)$ shared by a voxel of $B$ in the…
We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…
Despite a blossoming of research activity on racks and their homology for over two decades, with a record of diverse applications to central parts of contemporary mathematics, there are still very few examples of racks whose homology has…
We give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive…
We determine the ring structure of the loop homology of some global quotient orbifolds. We can compute by our theorem the loop homology ring with suitable coefficients of the global quotient orbifolds of the form $[M/G]$ for $M$ being some…
A combinatorial construction is used to analyze the properties of polyhedral products and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of…
We prove the existence of noncrossed product and indecomposable division algebras over the function field of a smooth p-adic curve, especially when the curve does not admit a smooth model over Z_p. Thus we generalize arXiv 0907.0670. To…
A gauge group is the topological group of automorphisms of a principal bundle. We compute the integral cohomology ring of the classifying spaces of gauge groups of principal U(n)-bundles over the 2-sphere by generalizing the operation for…
By using the loop orbifold of the symmetric product, we give a formula for the Poincar\'e polynomial of the free loop space of the Borel construction of the symmetric product. We also show that the Chas-Sullivan product structure in the…
In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we…