Related papers: An A-infinity operad in spineless cacti
Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to Deligne's conjecture on the Hochschild…
Using non-commutative differential forms, we construct a complex called singular Hochschild cochain complex for any associative algebra over a field. The cohomology of this complex is isomorphic to the Tate-Hochschild cohomology in the…
Motivated by string topology and the arc operad, we introduce the notion of quasi-operads and consider four (quasi)-operads which are different varieties of the operad of cacti. These are cacti without local zeros (or spines) and cacti…
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…
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…
In this note, we show that the normalized Hochschild co--chains of an associative algebra with a non--degenerate, symmetric, invariant inner product are an algebra over a chain model of the framed little discs operad which is given by…
We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…
We show that normalized cacti form an $\infty$-operad in the form of a dendroidal space satisfying a weak Segal condition. To do this, we introduce a new topological operad of bracketed trees and an enrichment of the dendroidal category…
The goal of this paper is to complete Getzler-Jones' proof of Deligne's Conjecture, thereby establishing an explicit relationship between the geometry of configurations of points in the plane and the Hochschild complex of an associative…
It is well known that the differential graded operad of A_infinity-algebras is a cofibrant replacement (a dg-resolution) of the operad of associative differential graded algebras without units. In this article we find a cofibrant…
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…
We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy…
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…
We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the A-infinity operad, yields…
We show that a model of chain complex of the free loop space of a $C^\infty$-manifold, which is proposed in arxiv:1404.0153, admits an action of a certain dg operad. This is a chain level structure under the Chas-Sullivan BV structure on…
The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the…
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…
The category of differential graded operads is a cofibrantly generated model category and as such inherits simplicial mapping spaces. The vertices of an operad mapping space are just operad morphisms. The 1-simplices represent homotopies…
The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (i.e., the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to…
The goal of this memoir is to prove that the bar complex B(A) of an E-infinity algebra A is equipped with the structure of a Hopf E-infinity algebra, functorially in A. We observe in addition that such a structure is homotopically unique…