A central extension of the form E : 0 → V → G → W → 0, where V and W are elementary abelian 2-groups, is called Bockstein closed if the components qi ∈ H ∗(W,F2) of the extension class of E generate an ideal which is closed under the Bockstein operator. In this paper, we study the cohomology ring of G when E is a Bockstein closed 2-power exact extension. The mod-2 cohomology ring of G has a sim...

In this paper we determine the ring structure of the Hochschild cohomology of truncated quiver algebras with the Yoneda product. On the one hand Locateli described the cohomology groups in terms of classes of pairs of paths using minimal resolutions. On the other hand, the Yoneda product has a nice description on the bar resolution as the usual cup product. Our first main result is the explicit...

Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the  local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,...

We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.

We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by Andruskiewitsch and Schneider of such Hopf algebras. Examples include all of Lusztig’s small quantum groups, whose cohomology was first computed explicitly by Gin...

Every homology or cohomology theory on a category of E∞ ring spectra is Topological André–Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A∞ ring spectra and for categories of algebras over many other operads.

We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras.

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

The main goal of this paper is to give a unified description for the structure of the small quantum cohomology rings for all homogeneous spaces of SL n (C). The quantum cohomology ring of a smooth projective variety, or, more generally of a symplectic manifold, has been introduced by physicists in the study of topo-logical field theories ([V], [W]). In the past few years, the highly non-trivial...

We construct a ring structure on complex cobordism tensored with Q, which is related to the usual ring structure as quantum cohomology is related to ordinary cohomology. The resulting object defines a generalized two-dimensional topological field theory taking values in a category of spectra.