General Theory of Lie Groupoids and Lie Algebroids available in Paperback
- Pub. Date:
- Cambridge University Press
This comprehensive modern account of the theory of Lie groupoids and Lie algebroids reveals their importance in differential geometry, in particular, their relations with Poisson geometry and general connection theory. It covers much research since the mid 1980s, including the first analysis in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. The volume will be of great interest to all learning the modern theory of Lie groupoids and Lie algebroids.
About the Author
Kirill Mackenzie is a reader in Pure Mathematics at the University of Sheffield
Table of Contents
Part I. The General Theory: 1. Lie groupoids: fundamental theory; 2. Lie groupoids: algebraic constructions; 3. Lie algebroids: fundamental theory; 4. Lie algebroids: algebraic constructions; Part II. The Transitive Theory: 5. Infinitesimal connection theory; 6. Path connections and Lie theory; 7. Cohomology and Schouten calculus; 8. The cohomological obstruction; Part III. The Poisson and Symplectic Theories: 9. Double vector bundles; 10. Poisson structures and Lie algebras; 11. Poisson and symplectic groupoids; 12. Lie bialgebroids; Appendix; Bibliography; Index.