© 2015

Formality Theory

From Poisson Structures to Deformation Quantization


Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 2)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Chiara Esposito
    Pages 1-5
  3. Chiara Esposito
    Pages 7-20
  4. Chiara Esposito
    Pages 21-59
  5. Chiara Esposito
    Pages 61-80
  6. Back Matter
    Pages 81-90

About this book


This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are the theory of Poisson manifolds, star products and their classification, deformations of associative algebras and the formality theorem. Readers will also be familiarized with the relevant physical motivations underlying the purely mathematical construction.


Formality Theory Hochshild Complex Hschild-Kostant-Rosenberg Theorem Kontsevich Formula Maurer-Cartan Equation Maurer-Cartan Equation Poisson Brackets Poisson Manifolds Poisson Manifolds Schouten Bracket

Authors and affiliations

  1. 1.Department of MathematicsUniversity of WürzburgWürzburgGermany

Bibliographic information


“The formality theorem gave deep insight into the homological algebra of smooth functions on a manifold. Many applications have grown out of this investigation, too many to mention here. … the author explains its implications together with its origins in the theory of quantization. This is a valuable contribution since the formulation of the statement requires some sophisticated preparation, which is carefully discussed in this booklet.” (Stefan Waldmann, Mathematical Reviews, February, 2016)