Introduction to foliations and lie groupoids

By:

Moerdijk, Izak

Contributor(s):

Mrcun, J

Material type: Book

BookSeries: Cambridge Studies in Advanced Mathematics ; Vol. 91Publication details: Cambridge: Cambridge University Press, 2003.Description: ix, 173 p. : ill. ; hb. ; 24 cmISBN:

9780521831970

Subject(s):

DDC classification:

514.72 MOE

Summary: 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.

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	514.72 MOE (Browse shelf(Opens below))	1	Available		030116

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Previous	514.3 WEE Shape of space	514.322 YAN Elementary point set topology: a transition to advanced mathematics	514.72 GEI Introduction to contact topology	514.72 MOE Introduction to foliations and lie groupoids	514.72 MUK Differential topology	514.72 WAL Differential topology: first steps	514.72 WAL Differential topology	Next

Includes bibliography and index.

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.

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