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Maurer–Cartan Methods in Deformation Theory

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Maurer–Cartan Methods in Deformation Theory

Maurer–Cartan Methods in Deformation Theory

The Twisting Procedure
Vladimir Dotsenko, Université de Strasbourg
Sergey Shadrin, Universiteit van Amsterdam
Bruno Vallette, Université Sorbonne Paris Nord
September 2023
Paperback
9781108965644
£47.99
GBP
Paperback
USD
eBook
    Description

    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.

    • Covers an exceptional range of treatments and topics
    • Starts and finishes with accessible surveys so that students and non-experts can quickly get into the core of the theory and appreciate the applications
    • Presents brand new ideas and methods, including a new treatment of the twisting procedure for operads

    Product details

    September 2023
    Paperback
    9781108965644
    150 pages
    229 × 153 × 11 mm
    0.27kg
    Available

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    Contents

    Table 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.
      • Show more

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    About the authors
      Authors
    • Vladimir Dotsenko , Université de Strasbourg

      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 , Universiteit van Amsterdam

      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 , Université Sorbonne Paris Nord

      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.

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