Related papers: Universal operations in Hochschild homology

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

We define a chain map of the form $\E(k)\otimes BA^{\otimes k}\longrightarrow BA$, where $\E$ is a combinatorial $E_\infty$-operad called the sequence operad, and $BA$ is the bar complex of an $\E$-algebra $A$. We see that Steenrod-type…

This thesis deals with the algorithmic representation of constructible sheaves of abelian groups on the \'etale site of a variety over an algebraically closed field, as well as the explicit computation of their cohomology. We describe three…

If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the…

We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.

Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by…

For a scheme X, we construct a sheaf C of complexes on X such that for every quasi-compact open subset U of X, C(U) is quasi-isomorphic to the Hochschild complex of the scheme U. Since C is moreover acyclic for taking sections on…

We describe all operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^* (in the case of a field of characteristic zero). We prove that such an…

The chain gravity properad introduced earlier by the author acts on the cyclic Hochschild of any cyclic $A_\infty$ algebra equipped with a scalar product of degree $-d$. In particular, it acts on the cyclic Hochschild complex of any…

The problem of constructing the explicit form for full twist deformations of simple Lie algebras g with twist carriers containing the maximal nilpotent subalgebra N^+(g) is studied. Our main tool is the sequence of regular subalgebras g_i…

We generalize a spectral sequence of Brun for the computation of topological Hochschild homology. The generalized version computes the $E$-homology of $THH(A;B)$, where $E$ is a ring spectrum, $A$ is a commutative $S$-algebra and $B$ is a…

The usual Laurent expansion of the analytic tensors on the complex plane is generalized to any closed and orientable Riemann surface represented as an affine algebraic curve. As an application, the operator formalism for the $b-c$ systems…

Examples of non-trivial higher string topology operations have been regrettably rare in the literature. In this paper, working in the context of string topology of classifying spaces, we provide explicit calculations of a wealth of…

In this paper we calculate the Hochschild cohomology of gentle $A_\infty$-algebras of arc collections on marked surfaces without boundary components. When the underlying arc collection has no loops or two-cycles, we show that the dgla…

Any finite-dimensional quasitriangular Hopf algebra $H$ can be formally extended to a ribbon Hopf algebra $\tilde H$ of twice the dimension. We investigate this extension and its representations. We show that every indecomposable $H$-module…

We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild (co)homology…

Let $X$ be a normal geometrically connected variety over a finite field $\kappa$ of characteristic~$p$. Let $E$ be a number field. Using automorphic methods over global function fields, we derive properties of the geometric monodromy groups…

The technique developed in Hochschild's works "Lie algebra kernels and cohomology " and "Cohomology classes of finite dimensional kernels for Lie algebras " [2],[3] can be applied to the special case of transitive Lie algebroids. Our task…

We introduce a finitely presented prop $\mathcal{S} = \{\mathcal{S}(n,m)\}$ in the category of differential graded modules whose associated operad $U(\mathcal{S})=\{\mathcal{S}(1,m)\}$ is a model for the $E_\infty$-operad. This finite…

We give a simple universal property of the multiplicative structure on the Thom spectrum of an $n$-fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax $\mathcal{O}$-monoidal…