In 1963 [Ann. of Math. 78, 267-288], Gerstenhaber invented a comp (osition) calculus in the
Hochschild complex of an associative algebra. In this paper, the first steps of the …

In this paper we prove that the sheaf of $\Lscr $-poly-differential operators for a locally free
Lie algebroid $\Lscr $ is formal when viewed as a sheaf of $ G_\infty $-algebras via …

Motivated by various developments in algebraic combinatorics and its applications, we
investigate here the fine structure of a fundamental but little known theorem, the …

We introduce the notion of a BV-operator∆={∆ n: V n→ V n− 1} n≥ 0 on a homotopy G-
algebra V• such that the Gerstenhaber bracket on H (V•) is determined by∆ in a manner …

A chain complex model for the free loop space of a connected, closed and oriented manifold
is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra …

We produce a master identity for a certain type of homotopy Gerstenhaber algebras, in
particular suitable for the prototype, namely the Hochschild complex of an associative …

We consider basic algebraic constructions associated with an abstract pre-operad, such as
a⌣-algebra, total composition•, pre-coboundary operator δ and tribrac {h, f, g}. A derivation …

In these notes, we define a new simplicial structure on a connected multiplicative operad
and call it connected multiplicative simplicial operad (for short; simplicial operad). Next we …

At the end of the nineteenth century, Poincaré created invariants to distinguish different
topological spaces and their features, foreshadowing the homology and cohomology groups …

In this paper, we revisit the formalism of graphs, trees, and surfaces which allows one to
build cell models for operads of algebraic interest and represent them in terms of a …