General theory of lie groupoids and lie algebroids / Kirill C.H. Mackenzie.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. Lie groupoids : fundamental theory -- 2. Lie groupoids : algebraic constructions -- 3. Lie algebroids : fundamental theory -- 4. Lie algebroids : algebraic constructions -- 5. Infinitesimal connection theory -- 6. Path connections and lie theory -- 7. Cohomology and Schouten calculus -- 8. The cohomological obstruction -- 9. Double vector bundles -- 10. Poisson structures and lie algebroids -- 11. Poisson and symplectic groupoids -- 12. Lie bialgebroids.

This 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.