LIE GROUPOIDS AND LIE ALGEBROIDS IN DIFFERENTIAL GEOMETRY by K. Mackenzie ( 9780521348829 )

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Title:

LIE GROUPOIDS AND LIE ALGEBROIDS IN DIFFERENTIAL GEOMETRY

By:

K. Mackenzie

Format:

Paperback

List price:

£88.00

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£77.00

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£11.00

ISBN 10:

052134882X

ISBN 13:

9780521348829

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

25 June, 1987

Series:

London Mathematical Society Lecture Note Series 124

Pages:

344

Description:

This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids.

Synopsis:

This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory.

Illustrations:

illustrations, bibliography, index

Publication:

Imprint:

Cambridge University Press

Returns:

Returnable

Some other items by this author:

CASE PRESENTATIONS IN OTOLARYNGOLOGY (PB)

GENERAL THEORY OF LIE GROUPOIDS AND LIE ALGEBROIDS (PB)

LIE GROUPOIDS AND LIE ALGEBROIDS IN DIFFERENTIAL GEOMETRY