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 GammaM, where M is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston?s eight geometries, and where Gamma < Isom(M) acts properly discontinuously. A general description of these geometric orbifolds is given and the closed oriented geometric 3-orbifolds with S3 as their underlying topological space are enumerated (except for hyperbolic orbifolds).
@article{urn:eudml:doc:43193,
title = {Geometric orbifolds.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {1},
year = {1988},
pages = {67-99},
zbl = {0655.57008},
mrnumber = {MR0977042},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43193}
}
Dunbar, William D. Geometric orbifolds.. Revista Matemática de la Universidad Complutense de Madrid, Tome 1 (1988) pp. 67-99. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43193/