Géométries modèles de dimension trois
Yves de Cornulier1
1 IRMAR Campus de Beaulieu 35042 Rennes cedex (France)
Séminaire de théorie spectrale et géométrie, Tome 27 (2008-2009), pp. 17-43.

On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.

In this expository article, we give a detailed proof of the classification by Thurston of the eight model geometries in dimension three.

DOI : 10.5802/tsg.269
Classification : 57M50, 22E40, 57M60
Mot clés : géométrie modèle, géométrie de Thurston, géométrisation
Keywords: model geometry, Thurston geometry, geometrization
Yves de Cornulier 1

1 IRMAR Campus de Beaulieu 35042 Rennes cedex (France) 
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Yves de Cornulier. Géométries modèles de dimension trois. Séminaire de théorie spectrale et géométrie, Tome 27 (2008-2009), pp. 17-43. doi : 10.5802/tsg.269. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.269/

[1] L. Bessières; G. Besson; M. Boileau; S. Maillot; J. Porti Geometrisation of 3-manifolds Livre en préparation (juin 2009)

[2] Laurent Bessières Conjecture de Poincaré : la preuve de R. Hamilton et G. Perelman, Gaz. Math. (2005) no. 106, pp. 7-35 | MR | Zbl

[3] Armand Borel Compact Clifford-Klein forms of symmetric spaces, Topology, Volume 2 (1963), pp. 111-122 | MR | Zbl

[4] Bruce Kleiner; John Lott Notes on Perelman’s papers, Geom. Topol., Volume 12 (2008) no. 5, pp. 2587-2855 | MR

[5] John W. Morgan Recent progress on the Poincaré conjecture and the classification of 3-manifolds, Bull. Amer. Math. Soc. (N.S.), Volume 42 (2005) no. 1, p. 57-78 (electronic) | MR | Zbl

[6] G. D. Mostow Self-adjoint groups, Ann. of Math. (2), Volume 62 (1955), pp. 44-55 | MR | Zbl

[7] Grigori Perelman The entropy formula for the Ricci flow and its geometric applications (2002) (arXiv/0211.5159) | Zbl

[8] Grigori Perelman Finite extinction time for the solutions to the Ricci flow on certain three-manifolds (2003) (arXiv/0307.5245) | Zbl

[9] Grigori Perelman Ricci flow with surgery on three-manifolds (2003) (arXiv/0303.5109) | Zbl

[10] Peter Scott The Geometries of 3-Manifolds, Bull. London Math. Soc., Volume 15 (1983) no. 5, pp. 401-487 | MR | Zbl

[11] William P. Thurston The Geometry and Topology of Three-Manifolds (1980) (Princeton University Notes)

[12] William P. Thurston Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.), Volume 6 (1982) no. 3, pp. 357-381 | MR | Zbl

[13] William P. Thurston Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series, 35, Princeton University Press, Princeton, NJ, 1997 (Edited by Silvio Levy) | MR | Zbl

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