This book gives a thorough and self-contained introduction to the theory of Hochschild
cohomology for algebras and includes many examples and exercises. The book then …

In this review article, first we give the concrete formulas of representations and
cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and …

The purpose of this paper is to complete Getzler-Jones' proof of Deligne's Conjecture,
thereby establishing an explicit relationship between the geometry of configurations of …

In this paper we prove that on a smooth algebraic variety the HKR-morphism twisted by the
square root of the Todd genus gives an isomorphism between the sheaf of poly-vector fields …

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 …

This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry,
topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment …

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 …

Let G be a compact connected Lie group and K a closed connected subgroup. Assume that
the order of any torsion element in the integral cohomology of G and K is invertible in a given …

Partial quotients of moment-angle complexes are topological analogues of smooth, not
necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for …

Covering an exceptional range of topics, this text provides a unique overview of the Maurer-
Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new …