相关论文: Multivariable cochain operations and little n-cube…

It was shown by Claus Scheiderer prior to 1994 that real closed spaces have \'{e}tale cohomology. Following Scheiderer, study of real closed spaces fell out of fashion and o-minimal geometry became the focus for those at the intersection of…

We show that the secondary Hochschild cohomology associated to a triple $(A,B,\varepsilon)$ has several of the properties of the usual Hochschild cohomology. Among others, we prove the existence of the cup and Lie products, discuss the…

We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{\ast} $-algebras associated to these groupoids. We provide a new…

For a von Neumann algebra M on a Hilbert space, A. Connes has constructed a module S and a derivation of M into S, such that M is approximately finite dimensional if and only if that derivation is inner. The paper contains a generalization…

We establish simplicial triviality of the convolution algebra $\ell^1(S)$, where $S$ is a band semigroup. This generalizes results of the first author [Glasgow Math. J. 2005, Houston J. Math. 2010]. To do so, we show that the cyclic…

The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…

In this paper we show that the relation between Kajiura-Stasheff's OCHA and A. Voronov's swiss-cheese operad is analogous to the relation between SH Lie algebras and the little discs operad. More precisely, we show that the OCHA operad is…

Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…

The reduced universal monoid on the action category associated to a pointed simplicial M-set has appeared in the guise of various simplicial monoid and group constructions. These include the classical constructions of Milnor and James, as…

For a pure bounded rationally cyclic subnormal operator $S$ on a separable complex Hilbert space $\mathcal H,$ J. B. Conway and N. Elias (Analytic bounded point evaluations for spaces of rational functions, J. Functional Analysis, 117:1{24,…

Nijenhuis operators are very useful in the deformation theory of algebras. In this paper, we introduce a new cohomology theory related to deformation of Nijenhuis algebra morphisms, this notion involves simultaneous deformation of two…

We show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of…

Hector, Mac\'{\i}as-Virg\'os, and Sanmart\'{\i}n-Carb\'on identified the complex of diffeological differential forms on the leaf space of a foliation with the complex of basic forms on the foliated manifold, yielding a canonical isomorphism…

Bihom-associative algebras have been recently introduced in the study of group hom-categories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain…

We review several well-known operads of compactified configuration spaces and construct several new such operads, C, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of…

For a large class of gauge theories a nilpotent BRS-operator $s$ is constructed and its cohomology in the space of local functionals of the off-shell fields is shown to be isomorphic to the cohomology of $\4s=s+d$ on functions $f(\4C,\PH)$…

Given an $N$-dimensional compact manifold $M$ and a field $\bk$, F. Cohen and L. Taylor have constructed a spectral sequence, $\cE(M,n,\bk)$, converging to the cohomology of the space of ordered configurations of $n$ points in $M$. The…

We prove an analog of the Deligne conjecture for prestacks. We show that given a prestack $\mathbb A$, its Gerstenhaber--Schack complex $\mathbf{C}_{\mathsf{GS}}(\mathbb A)$ is naturally an $E_2$-algebra. This structure generalises both the…

The aim of this paper is to construct an $E_\infty$-operad inducing an $E_\infty$-coalgebra structure on chain complexes with coefficients in $\mathbb{Z}$, which is an alternative description to the $E_\infty$-coalgebra by the Barrat-Eccles…

In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a…