相关论文: A combinatorial approach to Kontsevich's Swiss che…

For an associative algebra A we consider the pair "the Hochschild cochain complex C*(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show that this operad is quasi-isomorphic to the singular chain…

We prove a conjecture of Kontsevich which states that if $A$ is an $E_{d-1}$ algebra then the Hochschild cohomology object of $A$ is the universal $E_d$ algebra acting on $A$. The notion of an $E_d$ algebra acting on an $E_{d-1}$ algebra…

We introduce a new operad, which we call the Swiss-cheese operad. It mixes naturally the little disks and the little intervals operads. The Swiss-cheese operad is related to the configuration spaces of points on the upper half-plane and…

Let $A$ be a $1$-algebra. The Kontsevich Swiss Cheese conjecture [K2] states that the homotopy category $\mathrm{Ho}(\mathrm{Act}(A))$ of actions of $2$-algebras on $A$ has a final object and that this object is weakly equivalent to the…

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…

We describe combinatorial Hopf (co-)operadic models for the Swiss Cheese operads built from Feynman diagrams. This extends previous work of Kontsevich and Lambrechts-Voli\'c for the little disks operads.

In the present work, we extract pairs of topological spaces from maps between coloured operads. We prove that those pairs are weakly equivalent to explicit algebras over the one dimensional Swiss-Cheese operad SC_{1}. Thereafter, we show…

We study bicolored configurations of points in the Euclidean $n$-space that are constrained to remain either inside or outside a fixed Euclidean $m$-subspace, with $n - m \ge 2$. We define a higher-codimensional variant of the Swiss-Cheese…

We construct a set-theoretic coloured operad that may be thought of as a combinatorial model for the Swiss Cheese operad. This is the relative (or Swiss Cheese) version of the lattice path operad constructed by Batanin and Berger. By…

This is a revision of a paper first posted June 4, 2001. It will appear in the Journal of the AMS. In this paper we construct a small $E_\infty$ chain operad $\S$ which acts naturally on the normalized cochains $S^*X$ of a topological…

Let an n-algebra mean an algebra over the chain complex of the little n-cubes operad. We give a proof of Kontsevich's conjecture, which states that for a suitable notion of Hochschild cohomology in the category of n-algebras, the Hochschild…

We prove that the homology of the Swiss-cheese operad is a Koszul operad. As a consequence, we obtain that the spectral sequence associated to the stratification of the compactification of points on the upper half plane collapses at the…

We prove that if a pair of semi-cosimplicial spaces (X,Y) arise from a coloured operad then the semi-totalization sTot(Y) has the homotopy type of a relative double loop space and the pair (sTot(X),sTot(Y)) is weakly equivalent to an…

An affine action of an associative algebra $A$ on a vector space $V$ is an algebra morphism $A \to V \rtimes {\rm End}(V)$, where $V$ is a vector space and $V \rtimes {\rm End}(V)$ is the algebra of affine transformations of $V$. The one…

We show that the color restriction map $\mathrm{Op}^h({\mathcal{SC}}_m,{\mathcal{SC}}_n)\to \mathrm{Op}^h({\mathcal E}_{m-1},{\mathcal E}_{n-1})$ from the derived mapping space of Swiss cheese operads to that of little discs operads, is a…

We construct a 2-colored operad G^+ which, on the one hand, extends the operad G governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras (OCHA). We show that…

We build a model in groupoids for the Swiss-Cheese operad, based on parenthesized permutations and braids, and we relate algebras over this model to the classical description of algebras over the homology of the Swiss-Cheese operad. We…

Swiss cheese sets are compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Such sets have provided numerous counterexamples in the theory of uniform algebras. In this paper, we introduce a…

The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n-1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least…

Deligne asked in 1993 whether the Hochschild cochain complex of an associative ring has a natural action by the singular chains of the little 2-cubes operad. In this paper we give an affirmative answer to this question. We also show that…