Maurer-Cartan Methods in Deformation Theory - The Twisting Procedure

"This text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics, offering a new conceptual treatment of the twisting procedure. It includes many motivating examples to render the theory accessible to graduate students, as well as a survey of recent applications"--

List of contents

Introduction; 1. Maurer-Cartan methods; 2. Operad theory for filtered and complete modules; 3. Pre-Lie algebras and the gauge group; 4. The gauge origin of the twisting procedure; 5. The twisting procedure for operads; 6. Operadic twisting and graph homology; 7. Applications.

About the author

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.

Summary

This text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics, offering a new conceptual treatment of the twisting procedure. It includes many motivating examples to render the theory accessible to graduate students, as well as a survey of recent applications.

Product details

• Authors: Vladimir Dotsenko, Vladimir (Universite de Strasbourg) Dotsenko, Vladimir (Universite De Strasbourg) Shad Dotsenko, Dotsenko Vladimir, Sergey Shadrin, Sergey (Universiteit van Amsterdam) Shadrin, Bruno Vallette, Bruno (Universite Sorbonne Paris Nord) Vallette, Vallette Bruno
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 01.09.2023
• EAN: 9781108965644
• ISBN: 978-1-108-96564-4
• No. of pages: 150
• Series: London Mathematical Society Lecture Note Series; London Mathematical Society Le
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Algebra, MATHEMATICS / Topology, geometry, Algebraic Geometry, Mathematical physics, Algebraic Topology