Maurer-Cartan methods in deformation theory : the twisting procedure / Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette.

Format:

Book

Author/Creator:

Dotsenko, Vladimir, 1981- author.

Shadrin, Sergey, 1980- author.

Vallette, Bruno, author.

Series:

London Mathematical Society lecture note series ; 488.

London Mathematical Society lecture note series ; 488

Language:

English

Subjects (All):

Lie algebras.

Twist mappings (Mathematics).

Operads.

Deformations of singularities.

Physical Description:

1 online resource (viii, 177 pages) : digital, PDF file(s).

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2024.

Summary:

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.

Contents:

Maurer-Cartan methods

Operad theory for filtered and complete modules

Pre-Lie algebras and the gauge group

The gauge origin of the twisting procedure

The twisting procedure for operads

Operadic twisting and graph homology

Applications.

Notes:

Title from publisher's bibliographic system (viewed on 22 Aug 2023).

Other Format:

Print version:

ISBN:

9781108963800 (ebook)

Access Restriction:

Restricted for use by site license.