Full paper in PDF:
$% W. D. Dunbar, Geometric orbifolds, Rev. Mat. Univ. Complut. Madrid 1 (1988), no. 1, 2, 3, 67–99.%$

Geometric Orbifolds

William D. DUNBAR
Department of Mathematics
University of Michigan
Ann Arbor, Michigan 48109-1003 -- USA

Received: March 31, 1986
Revised: December 1, 1987

An orbifold is a topological space which “locally looks like” the orbit space of a properly discontinuous group action on a manifold. After a brief review of basic concepts, we consider the special case 3-dimensional orbifolds of the form G\M  , where M  is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston’s eight geometries, and where G < Isom(M)  acts properly discontinuously. A general description of these geometric orbifolds is given and the closed oriented geometric 3-orbifolds with   3
S  as their underlying topological space are enumerated (except for hyperbolic orbifolds.

1980 Mathematics Subject Classification (1985 revision): 22E40.