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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.
- Sales Rank: #3421849 in eBooks
- Published on: 2003-09-18
- Released on: 2003-09-18
- Format: Kindle eBook
Review
"This book, though relatively short, is packed with interesting information. The student who would like a brief but substantial introduction to foliation theory will find it rewarding, but should be prepared for some hard work. There are many exercises, often challenging, and these illuminate the ideas and sometimes incorporate significant steps of proofs." Bulletin of the American Mathematical Society
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