Three-dimensional orbifolds and their geometric structures / Michel Boileau, Sylvain Maillot, Joan Porti

Bibliogr. p. [149]-163. Index

This well-written monograph presents the extensive background theory and results needed for the Orbifold Theorem, and finishes with a detailed outline of the proof in the important special case when the orbifold is closed and all local groups are cyclic. The background includes Thurston's eight geometries, the topological theory of 2- and 3-dimensional orbifolds, fibered structures on 3-orbifolds, factorization of 3-orbifolds into irreducible orbifolds, Haken orbifolds and their toric splittings, geometrization of Seifert orbifolds, hyperbolic structures and the associated representation varieties, hyperbolic Dehn filling of orbifolds, and cone manifolds and their deformation theory. Some of these are straightforward adaptations of corresponding concepts from the theory of 3-manifolds, but many require significant technical innovations which have been developed by the authors and others. Extensive citations are included; the bibliography lists well over two hundred references. (Zentralblatt)