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 …

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 …

This book brings together both the classical and current aspects of deformation theory. The
presentation is mostly self-contained, assuming only basic knowledge of commutative …

This paper provides a conceptual study of the twisting procedure, which amounts to create
functorially new differential graded Lie algebras, associative algebras or operads (as well as …

The Duflo isomorphism first appeared in Lie theory and representation theory. It is an
isomorphism between invariant polynomials of a Lie algebra and the center of its universal …

The Kontsevich deformation quantization combines Poisson dynamics, noncommutative
geometry, number theory, and calculus of oriented graphs. To manage the algebra and …

The Kontsevich deformation quantization combines Poisson dynamics, noncommutative
geometry, number theory, and calculus of oriented graphs. To manage the algebra and …

First three sections of this overview paper cover classical topics of deformation theory of
associative algebras and necessary background material. We then analyze algebraic …

We study the homotopy theory of the wheeled prop controlling Poisson structures on formal
graded finite-dimensional manifolds and prove, in particular, that the Grothendieck …

Operads are mathematical devices that describe algebraic structures of many varieties and
in various categories. Operads are particularly important in categories with a good notion of …