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

Auteur principal : Boileau, Michel, 1953-, AuteurCo-auteur : Maillot, Sylvain, Auteur • Porti, Joan, 1967-, AuteurType de document : MonographieCollection : Panoramas et synthèses, 15Langue : anglais.Pays : France.Éditeur : Paris : Société Mathématique de France, 2003Description : 1 vol. (VIII-167 p.) : fig. ; 24 cmISBN : 285629152X.ISSN : 1272-3835.Bibliographie : Bibliogr. p. [149]-163. Index.Sujet MSC : 57M50, General low-dimensional topology, General geometric structures on low-dimensional manifolds
53C23, Global differential geometry, Global geometric and topological methods; differential geometric analysis on metric spaces
57M60, General low-dimensional topology, Group actions on manifolds and cell complexes in low dimensions
57-02, Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
En-ligne : Sommaire
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Séries Panor 15 (Browse shelf) Available 02658-01

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)

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