General Theory of Lie Groupoids and Lie Algebroids [Paperback]

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry.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 andgeneral 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 such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.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 andgeneral 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 such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.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.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 obstructlÃu