Given an algebra with a group G-action, we construct brace structures for its G-twisted
Hochschild cochains. An an application, we construct G-Frobenius algebras for orbifold …

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector
space X. The result implies, in particular, that the Kontsevich deformation quantizations of S …

QUANTIZATION OF LIE BIALGEBRAS VIA THE FORMALITY OF THE OPERAD OF LITTLE
DISKS Dmitry Tamarkin 1 Introduction Page 1 GAFA, Geom. funct. anal. Vol. 17 (2007) 537 …

We show that any homotopy Gerstenhaber algebra is naturally a strongly homotopy
commutative (shc) algebra in the sense of Stasheff–Halperin with a homotopy associative …

In these lectures we present our minimality theorem by which in cohomology of a topological
space appear multioperations which turn it ot Stasheff $ A (\infty) $ algebra. This rich …

We show that Hochschild cohomology of an algebra over a field is a space of infinity
coderivations on an arbitrary projective bimodule resolution of the algebra. The …

Based on the Gerstenhaber Theory, clarification is made of how operadic dynamics may be
introduced. Operadic observables satisfy the Gerstenhaber algebra identities and their time …

We show that the celebrated operad of pre-Lie algebras is very rigid: it has no “non-obvious”
degrees of freedom from either of the three points of view: deformations of maps to and from …

Given an n-manifold M and an n-category C, we define a chain complex (the" blob complex")
B_*(M; C). The blob complex can be thought of as a derived category analogue of the Hilbert …

We summarize our axioms for higher categories, and describe the “blob complex.” Fixing an
n-category, the blob complex associates a chain complex to any n-manifold W. The zeroth …