Related papers: Kontsevich's Swiss Cheese Conjecture

In this note, we define the notion of a cactus set, and show that its geometric realization is naturally an algebra over Voronov's cactus operad, which is equivalent to the framed 2-dimensional little disks operad $\mathcal{D}_2$. Using…

In this paper, we give an explicit chain map, which induces the algebra isomorphism between the Hochschild cohomology ${\bf HH}^{\bullet}(B)$ and the $H$-invariant subalgebra ${\bf H}^{\bullet}(A, B)^{H}$ under two mild hypotheses, where…

We make use of the cotangent complex formalism developed by Lurie to formulate Quillen cohomology of algebras over an enriched operad. Additionally, we introduce a spectral Hochschild cohomology theory for enriched operads and algebras over…

We will consider P-graph complexes, where P is a cyclic operad. P-graph complexes are natural generalizations of Kontsevich's graph complexes -- for P = the operad for associative algebras it is the complex of ribbon graphs, for P = the…

The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison…

We prove the statement in the title, solving in this way a conjecture stated by Ginot for manifolds with corners. Along the way, we establish a derived Swiss-cheese additivity theorem and an alternative proof for the hyperdescent of…

In this paper we study the homology of 2 versions of the swiss-cheese operad. We prove that the zeroth homology of these two versions are Koszul operads and relate this to strong homotopy Lebiniz pairs and OCHA, defined by Kajiura and…

In the formulation of his celebrated Formality conjecture, M. Kontsevich introduced a universal version of the deformation theory for the Schouten algebra of polyvector fields on affine manifolds. This universal deformation complex takes…

In the first part, we give an explicit description of the cotangent complex of differential graded (dg) operads, modeled as an operadic infinitesimal bimodule. This leads to a uniform formula for the Quillen cohomology of their associated…

For a finite-dimensional Lie algebra $\mathfrak g$ over a field $\mathbb K\supset \mathbb C$, we deduce from the compatibility between cup products Kontsevich (2003, Section 8) and from the main result of Shoikhet (2001) an alternative way…

It is observed that Kaygun's Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, (i) an analogue of Deligne's Conjecture holds for module-algebras, and (ii) the Hopf-Hochschild…

It is shown that every algebra over the chain operad of the little disks operad gives naturally rise to a Hertling-Manin's F-manifold, that is a smooth manifold equipped with an integrable graded commutative associative product on the…

A theory of allocation maps has been developed by J. F. Feinstein and M. J. Heath in order to prove a theorem, using Zorn's lemma, concerning the compact plane sets known as Swiss cheese sets. These sets are important since, as domains,…

In this paper we consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We introduce a notion of 'allocation map' connected with Swiss…

We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work…

The main goal of this paper is to investigate the structure of Hopf algebras with the property that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. In order to do that we define the Hochschild cohomology of an…

First we describe a class of homotopy Frobenius algebras via cyclic operads which we call cyclic $A_\infty$ algebras. We then define a suitable new combinatorial operad which acts on the Hochschild cochains of such an algebra in a manner…

The notion of a coalgebra measuring, introduced by Sweedler, is a kind of generalized ring map between algebras. We begin by studying maps on Hochschild homology induced by coalgebra measurings. We then introduce a notion of coalgebra…

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to…

We give a new computation of Hochschild (co)homology of the exterior algebra, together with algebraic structures, by direct comparison with the symmetric algebra. The Hochschild cohomology is determined to be essentially the algebra of…