Introduction to Foliations and Lie Groupoids

This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.Table of ContentPreface; Prerequisites; 1. Foliations; 2. Holonomy and stability; 3. Two classical theorems; 4. Molino's theory; 5. Lie groupoids; 6. Lie algebroids; References and further reading; Index.Review Quote'The book is based on course lecture notes and it still keeps its qualities and nice presentation.' EMS NewsletterReview Quote'The book by Moerdijk and Mrcun serves as a concise and user-friendly introduction to the foundations of foliation theory and Lie groupoids, delving into just about all of the above-mentioned facets of the subject, and more. … the book reflects a great deal of care and thought on the part of the authors. … there is no apparent neglect of essential details, and the clarity of exposition is maintained right to the end. Those interested in the subject should find the book a delight to work through, and should thereby find a pathway into the more specialized topics mentioned earlier. … the treatment of each topic is as admirably self-contained as one might hope for. The instructional value of the book seems quite high, and it could certainly be recommended as text on which to base a graduate course.' Bulletin London Math SocietyA quick introduction to foliations and Lie groupoids with numerous examples and exercises to aid the reader.