Orbifolds as groupoids: an introduction. (English) Zbl 1041.58009

Adem, Alejandro (ed.) et al., Orbifolds in mathematics and physics. Proceedings of a conference on mathematical aspects of orbifold string theory, Madison, WI, USA, May 4–8, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2990-4/pbk). Contemp. Math. 310, 205-222 (2002).
This is a well-written paper of introductory nature, the main purpose of which is to describe orbifolds in terms of a certain kind of groupoids. The author starts with basic concepts concerning Lie groupoids and Morita equivalence. A groupoid is called a foliation groupoid, if each isotropy group is discrete. An orbifold groupoid is defined as a proper foliation groupoid. Then the category of orbifolds and structures over orbifolds are studied. Special attention is paid to cohomologgy and inertia groupoids.
For the entire collection see [Zbl 1003.00015].


58H05 Pseudogroups and differentiable groupoids
22A22 Topological groupoids (including differentiable and Lie groupoids)
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