General Theory of Lie Groupoids and Lie Algebroids

Kirill Mackenzie - Collection London Mathematical Society Student Texts

740 pages, parution le 07/06/2005

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Résumé

This is a comprehensive modern 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 including 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 trivial 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.

Book includes many results which have never appeared in book form before
Massive expansion of a successful earlier book
A thorough and detailed account of the subject

L'auteur - Kirill Mackenzie

Kirill Mackenzie : University of Sheffield

Sommaire

I. The General Theory
- 1. Lie groupoids: fundamental theory
- Lie groupoids: algebraic constructions
- Lie algebroids: fundamental theory
- Lie algebroids: algebraic constructions
II. The Transitive Theory
- Infinitesimal connection theory
- Path connections and Lie theory
- Cohomology and Schouten calculus
- The cohomological obstruction
III. The Poisson and Symplectic Theories
- Double vector bundles
- Poisson structures and Lie algebroids
- Poisson and symplectic groupoids
- Lie bialgebroids
- Appendix
- Bibliography

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Kirill Mackenzie
Collection	London Mathematical Society Student Texts
Parution	07/06/2005
Nb. de pages	740
Format	15 x 22,5
Couverture	Broché
Poids	500g
Intérieur	Noir et Blanc
EAN13	9780521499286
ISBN13	978-0-521-49928-6