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 immidiate 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 folliations then proseeds 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 contex 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.
Type of material - scientific monograph
; adult, serious
Edition - Reprinted
Publication and manufacture - New York : Cambridge University Press, 2005
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