General theory of Lie groupoids and Lie algebroids

Kirill C H Mackenzie

• Contents, Prologue, Introduction and Preface (30 pages)
• PART I: The general theory
  • Lie groupoids: fundamental theory
  • Chapter 2:- Lie groupoids: algebraic constructions (31 pages)
  • Lie algebroids: fundamental theory
  • Lie algebroids: algebraic constructions
• PART II: The locally trivial theory
  • Infinitesimal connection theory
  • Path connections
  • Cohomology and Schouten Calculus for Lie algebroids
  • The cohomological obstruction
• PART III: The symplectic and Poisson theory
  • Double vector bundles and their duality
  • Poisson structures and Lie algebroids
  • Poisson groupoids and symplectic groupoids
  • Lie bialgebroids
• Appendix

Cover blurb: This is a comprehensive and up to date 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 and includes 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 trival 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.

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