General theory of Lie groupoids and Lie algebroids

Kirill C H Mackenzie

General Theory of Lie Groupoids and Lie Algebroids,
Cambridge University Press London Mathematical Society Lecture Note Series 213.
2005, xxxviii + 501 pages, ISBN 0541499283
Review by Th. Th. Voronov in Bull. London Math. Soc. 42, 185--190, 2010.

Cover blurb: This is a comprehensive and up to date account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry and general connection theory. It covers much work done since the mid 1980s and includes the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles, as well as a revised account of the relations between locally trival Lie groupoids, Atiyah sequences, and connections in principal bundles. As such, this book will be of great interest to all those concerned with the use of Poisson geometry as a semi-classical limit of quantum geometry, as well as to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.

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April 2010

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