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

Geometric Orbifolds

William D. DUNBAR

Department of Mathematics

University of Michigan

Ann Arbor, Michigan 48109-1003 -- USA

University of Michigan

Ann Arbor, Michigan 48109-1003 -- USA

Revised: December 1, 1987

ABSTRACT

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 , where is a simply-connected 3-dimensional homogeneous space corresponding to one of Thurston’s eight geometries, and where acts properly discontinuously. A general description of these geometric orbifolds is given and the closed oriented geometric 3-orbifolds with as their underlying topological space are enumerated (except for hyperbolic orbifolds.

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