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Lie groupoid

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∞-Lie theory

Context

∞-Lie groupoids

Examples

∞-Lie algebroids

Examples

Integration and differentiation

Cohomology

∞-Chern-Weil theory

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Contents

Definition

A Lie groupoid is an internal groupoid in Diff.

There are these and those conditions on the various maps involved…

Literature

Topological and differentiable (or smooth, “Lie”) groupoids (and more generally categories) were introduced in

  • C. Ehresmann Colloque de Géometrie Differentielle Globale (Bruxelles, 1958), 137–150, Centre Belge Rech. Math., Louvain, 1959;

Reviews and developments of the theory of Lie groupoids include

  • Pradines, ….

  • K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, Cambridge University Press, 2005, xxxviii + 501 pages (website)

  • K. C. H. Mackenzie, Lie groupoids and Lie algebroids in differential geometry, London Mathematical Society Lecture Note Series, 124. Cambridge University Press, Cambridge, 1987. xvi+327 pp (MathSciNet)

Further discussion

John Baez talks about various kinds of Lie groupoids in TWF 256.

Revised on December 16, 2009 17:39:24 by Urs Schreiber (193.198.162.13)
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