Related papers: OCHA and the swiss-cheese operad
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…
The operad of framed little discs is shown to be equivalent to a cyclic operad. This answers a conjecture of Salvatore in the affirmative, posed at the workshop `Knots and Operads in Roma,' at Universita di Roma ``La Sapienza'' in July of…
We describe new graphical models of the framed little disks operads which exhibit large symmetry dg Lie algebras.
We study $\mathcal{O}$-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of $\mathcal{O}$-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter…
We show that Kontsevich's formality of the little disk operad, obtained using graphs, is homotopic to Tamarkin's formality, for a special choice of a Drinfeld associator. The associator is given by parallel transport of the…
This paper gives a systematic study of matching dialgebras corresponding to the operad $As^{(2)}$ in \cite{Zi} as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close…
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…
A theorem of Kontsevich relates the homology of certain infinite dimensional Lie algebras to graph homology. We formulate this theorem using the language of reversible operads and mated species. All ideas are explained using a pictorial…
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…
For $\mathcal{O}$ a reduced operad, a generalized divergence from the derivations of a free $\mathcal{O}$-algebra to a suitable trace space is constructed. In the case of the Lie operad, this corresponds to Satoh's trace map and, for the…
A simplicial cochain complex can be derived from a locally small poset by taking the nerve of the poset viewed as a category. We show that the simplicial cochain complex and a relative Hochschild cochain complex of the incidence algebra of…
We study ordered configuration spaces of compact manifolds with boundary. We show that for a large class of such manifolds, the real homotopy type of the configuration spaces only depends on the real homotopy type of the pair consisting of…
The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three different definitions of higher order…
We prove that every open-closed homotopy algebra, introduced by Kajiura and Stasheff (arXiv: archive/0410291), naturally gives rise to an open-closed version of Hochschild cochain complex whose cohomology admits a canonical Gerstenhaber…
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 define a generalization of Massey products for algebras over a Koszul operad in characteristic zero, extending Massey's and Allday's and Retah's in the associative and Lie cases, respectively. We establish connections with minimal models…
his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem…
We show that the family of chain modules over the standard simplices can be equipped with an operad structure. Similarly, the family of cochain modules of the Stasheff polytopes can be equipped with an operad structure. We first show that…
It is known that a model for the differential graded algebra (dga) of differential forms on the free loop space $LN$ of a simply connected smooth manifold $N$ is given by the Hochschild chain complex of the dga $\Omega(N)$ of differential…
It is clarified how cohomologies and Gerstenhaber algebras can be associated with linear pre-operads (comp algebras). Their relation to mechanics and operadic physics is concisely discussed.