Maurer-Cartan Methods in Deformation Theory

The Twisting Procedure

AvVladimir Dotsenko,Sergey Shadrin

Häftad, Engelska, 2023

Del 488 i serien London Mathematical Society Lecture Note Series

639 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-09-07
Mått:153 x 229 x 11 mm
Vikt:270 g
Format:Häftad
Språk:Engelska
Serie:London Mathematical Society Lecture Note Series
Antal sidor:186
Förlag:Cambridge University Press
ISBN:9781108965644

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

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.

Innehållsförteckning

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.