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

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

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

DOI: 10.5802/tsg.269
Classification: 57M50, 22E40, 57M60
Keywords: 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) 
@article{TSG_2008-2009__27__17_0,
     author = {Yves de Cornulier},
     title = {G\'eom\'etries mod\`eles de dimension trois},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {17--43},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {27},
     year = {2008-2009},
     doi = {10.5802/tsg.269},
     mrnumber = {2799145},
     language = {fr},
     url = {https://tsg.centre-mersenne.org/articles/10.5802/tsg.269/}
}
TY  - JOUR
AU  - Yves de Cornulier
TI  - Géométries modèles de dimension trois
JO  - Séminaire de théorie spectrale et géométrie
PY  - 2008-2009
SP  - 17
EP  - 43
VL  - 27
PB  - Institut Fourier
PP  - Grenoble
UR  - https://tsg.centre-mersenne.org/articles/10.5802/tsg.269/
DO  - 10.5802/tsg.269
LA  - fr
ID  - TSG_2008-2009__27__17_0
ER  - 
%0 Journal Article
%A Yves de Cornulier
%T Géométries modèles de dimension trois
%J Séminaire de théorie spectrale et géométrie
%D 2008-2009
%P 17-43
%V 27
%I Institut Fourier
%C Grenoble
%U https://tsg.centre-mersenne.org/articles/10.5802/tsg.269/
%R 10.5802/tsg.269
%G fr
%F TSG_2008-2009__27__17_0
Yves de Cornulier. Géométries modèles de dimension trois. Séminaire de théorie spectrale et géométrie, Volume 27 (2008-2009), pp. 17-43. doi : 10.5802/tsg.269. https://tsg.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

Cited by Sources: