Maurer-Cartan Methods in Deformation Theory

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 conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.

Author Biography

Vladimir Dotsenko is Professor at the University of Strasbourg and Junior Member of the Institut Universitaire de France. His research focuses on homotopical algebra and its applications in areas including category theory, combinatorics and ring theory. Sergey Shadrin is Professor of Geometry and Mathematical Physics at the University of Amsterdam. His main research interests include enumerative geometry, homotopical algebra, integrable hierarchies, and topological recursion. Bruno Vallette is Professor of Mathematics at the Université Sorbonne Paris Nord and was previously Junior Member of the Institut Universitaire de France. He co-authored the book ‘Algebraic Operads’ (2012) with Jean-Louis Loday, which is now the reference on this topic.