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Cubical cochains are equipped with an associative product, dual to the Serre diagonal, lifting the graded ring structure in cohomology. In this work we introduce through explicit combinatorial methods an extension of this product to a full $E_infty$-structure. We also study the Cartan-Serre map relating the cubical and simplicial singular cochains of spaces, and prove that this classical map is a quasi-isomorphism of $E_infty$-algebras.
We investigate when a commutative ring spectrum $R$ satisfies a homotopical version of local Gorenstein duality, extending the notion previously studied by Greenlees. In order to do this, we prove an ascent theorem for local Gorenstein duality along
The solution of Delignes conjecture on Hochschild cochains and the formality of the operad of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the Hochschild cochains of an associative algebra. In this paper we constr
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category. This is the most technical among the axioms for S to be an exce
The theory of abstract kernels in non-trivial extensions for many kinds of algebraical objects, such as groups, rings and graded rings, associative algebras, Lie algebras, restricted Lie algebras, DG-algebras and DG-Lie algebras, has been widely stud
We compute the $C_p$-equivariant dual Steenrod algebras associated to the constant Mackey functors $underline{mathbb{F}}_p$ and $underline{mathbb{Z}}_{(p)}$, as $underline{mathbb{Z}}_{(p)}$-modules. The $C_p$-spectrum $underline{mathbb{F}}_p otimes u