A proof of Thurston's uniformization theorem of geometric orbifolds.
| dc.contributor.author | Matsumoto, Yukio | |
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-20T18:47:16Z | |
| dc.date.available | 2023-06-20T18:47:16Z | |
| dc.date.issued | 1991 | |
| dc.description.abstract | The authors prove that every geometric orbifold is good. More precisely, let X be a smooth connected manifold, and let G be a group of diffeomorphisms of X with the property that if any two elements of G agree on a nonempty open subset of X, then they coincide on X. If Q is an orbifold which is locally modelled on quotients of open subsets of X by finite subgroups of G, then the authors prove that the universal orbifold covering of Q is a (G,X)-manifold. A similar theorem was stated, and the proof sketched, in W. Thurston's lecture notes on the geometry and topology of 3-manifolds. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22135 | |
| dc.identifier.doi | 10.3836/tjm/1270130498 | |
| dc.identifier.issn | 0387-3870 | |
| dc.identifier.officialurl | http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.tjm/1270130498 | |
| dc.identifier.relatedurl | http://projecteuclid.org/DPubS?Service=UI&version=1.0&verb=Display&handle=euclid | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58616 | |
| dc.issue.number | 1 | |
| dc.journal.title | Tokyo Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 196 | |
| dc.page.initial | 181 | |
| dc.publisher | Departments of Mathematics of Gakushuin University | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | finite group action | |
| dc.subject.keyword | orbifold covering | |
| dc.subject.keyword | geometry | |
| dc.subject.ucm | Topología | |
| dc.subject.ucm | Geometría | |
| dc.subject.unesco | 1210 Topología | |
| dc.subject.unesco | 1204 Geometría | |
| dc.title | A proof of Thurston's uniformization theorem of geometric orbifolds. | |
| dc.type | journal article | |
| dc.volume.number | 14 | |
| dcterms.references | A. D. ALEKSANDROV, On completion of a space by polyhedra, Vestnik Leningrad Univ. Ser. Math. Fiz. Khim., 9:2 (1954), 33-43. F. BONAHON and L. SIEBENMANN, The classification of Seifert fibered 3-orbifolds, Low Dimensional Topology, ed. by R. Fenn, London Math. Soc. Lecture Note Series, 85(1985),19-85. A. DRESS, Newman’s theorems on transformation groups, Topology, 8 (1969), 203-207. W. D. DUNBAR, Geometric orbifolds, Revista Mat. Univ. Compl. Madrid, 1 (1988), 67-99. R. H. Fox, Covering spaces with singularities, Algebraic Geometry and Topology,Princeton Univ. Press (1957), 243-257. J. H. V. HUNT, Branched coverings as uniform completions of unbranched coverings (Résumé), Contemporary Math., 12 (1982), 141-155. M. KATO, On uniformization of orbifolds, Adv. Stud. Pure Math., 9 (1986), 149-172. B. MASKIT, On Poincare’s theorem for fundamental polygons, Adv. in Math., 7 (1971), 219-230. J. M. MoNTESINOS, Sobre la conjetura de Poincar\’e y los recubridores ramificados sobre un nudo, Ph. D. Theses, Univ. Compl. Madrid (1971). L. P. NEUWIRTH, Knot Groups, Ann. Math. Stud., 56 (1965), Princeton Univ. Press. M. H. A. NEWMAN, A theorem on periodic transformations of spaces, Quart. J. Math., 2 (1931), 1-8. I. SATAKE, On a generalization of the notion of manifolds, Proc. Nat. Acad. Sci. USA, 42 (1956), 359-363. H. SEIFERT, Komplexe mit Seitenzuordenung, Nachr. Akad. Wiss. Göttingen Math. Phys. Kl. II, 6 (1975), 49-80. W. THURSTON, The Geometry and Topology of 3-Manifolds, preprint, Princeton, 1976-79. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
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