Some applications of Ricci flow to 3-manifolds
Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 121-148.
DOI: 10.5802/tsg.251
Maillot, Sylvain 1

1 Université Louis Pasteur Institut de Recherche Mathématique Avancée 7 rue René Descartes 67084 Strasbourg cedex (France)
@article{TSG_2006-2007__25__121_0,
     author = {Maillot, Sylvain},
     title = {Some applications of {Ricci} flow to 3-manifolds},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {121--148},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {25},
     year = {2006-2007},
     doi = {10.5802/tsg.251},
     zbl = {1159.53338},
     mrnumber = {2478812},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/tsg.251/}
}
TY  - JOUR
AU  - Maillot, Sylvain
TI  - Some applications of Ricci flow to 3-manifolds
JO  - Séminaire de théorie spectrale et géométrie
PY  - 2006-2007
SP  - 121
EP  - 148
VL  - 25
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/tsg.251/
DO  - 10.5802/tsg.251
LA  - en
ID  - TSG_2006-2007__25__121_0
ER  - 
%0 Journal Article
%A Maillot, Sylvain
%T Some applications of Ricci flow to 3-manifolds
%J Séminaire de théorie spectrale et géométrie
%D 2006-2007
%P 121-148
%V 25
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/tsg.251/
%R 10.5802/tsg.251
%G en
%F TSG_2006-2007__25__121_0
Maillot, Sylvain. Some applications of Ricci flow to 3-manifolds. Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 121-148. doi : 10.5802/tsg.251. http://www.numdam.org/articles/10.5802/tsg.251/

[1] Anderson, Michael Scalar curvature and the existence of geometric structures on 3-manifolds. I, J. Reine Angew. Math., Volume 553 (2002), pp. 125-182 | MR | Zbl

[2] Angenent, Sigurd; Knopf, Dan An example of neckpinching for Ricci flow on S n+1 , Math. Res. Lett., Volume 11 (2004) no. 4, pp. 493-518 | MR | Zbl

[3] Bessières, Laurent; Besson, Gérard; Boileau, Michel; Maillot, Sylvain; Porti, Joan Géométrisation des variétés de dimension 3 (In preparation.)

[4] Bessières, Laurent; Besson, Gérard; Boileau, Michel; Maillot, Sylvain; Porti, Joan Weak collapsing and geometrisation of aspherical 3-manifolds, ArXiv:0706.2065, 2007

[5] Besson, Gérard Preuve de la conjecture de Poincaré en déformant la métrique par la courbure de Ricci (d’après Perelman), Séminaire Bourbaki 2004-2005 (Astérisque), Volume 307, Société Mathématique de France, Paris, France, 2006, pp. 309-348

[6] Boileau, Michel Uniformisation en dimension trois, Astérisque, Volume 266 (2000), pp. Exp. No. 855, 4, 137-174 (Séminaire Bourbaki, Vol. 1998/99) | Numdam | MR | Zbl

[7] Boileau, Michel; Maillot, Sylvain; Porti, Joan Three-dimensional orbifolds and their geometric structures, Panoramas et Synthèses, 15, Société Mathématique de France, Paris, 2003 | MR | Zbl

[8] Cao, Huai-Dong; Zhu, Xi-Ping A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow, Asian Journal of Mathematics, Volume 10 (2006) no. 2, pp. 165-492 (Revised version available on the arXiv) | MR

[9] Casson, Andrew; Jungreis, Douglas Convergence groups and Seifert fibered 3-manifolds, Invent. Math., Volume 118 (1994), pp. 441-456 | MR | Zbl

[10] Cheeger, Jeff; Gromov, Michael Collapsing riemannian manifolds while keeping their curvature bounded I, J. Differential Geometry, Volume 23 (1986), pp. 309-346 | MR | Zbl

[11] Cheeger, Jeff; Gromov, Michael Collapsing riemannian manifolds while keeping their curvature bounded II, J. Differential Geometry, Volume 32 (1990), pp. 269-298 | MR | Zbl

[12] Chow, Bennett; Knopf, Dan The Ricci flow : an introduction, Mathematical surveys and monographs, 110, A.M.S., 2004 | MR | Zbl

[13] Colding, Tobias H.; Minicozzi, William P. II Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman, J. Amer. Math. Soc., Volume 18 (2005) no. 3, p. 561-569 (electronic) | MR | Zbl

[14] Colding, Tobias H.; Minicozzi, William P. II Width and finite extinction time of Ricci flow, ArXiv:0707.0108, 2007

[15] Fukaya, Kenji Collapsing Riemannian manifolds and its applications, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, Tokyo (1991), pp. 491-500 | MR | Zbl

[16] Gabai, David Convergence groups are Fuchsian groups, Annals of Math., Volume 136 (1992), pp. 447-510 | MR | Zbl

[17] Gromov, M. Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math., Volume 56 (1982), p. 5-99 (1983) | Numdam | MR | Zbl

[18] Gromov, Michael Hyperbolic manifolds (according to Thurston and Jørgensen), Bourbaki Seminar, Vol. 1979/80 (Lecture Notes in Math.), Volume 842, Springer, Berlin, 1981, pp. 40-53 | Numdam | MR | Zbl

[19] Gromov, Michael; Lawson, Blaine Jr Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math., Volume 58 (1983), p. 83-196 (1984) | Numdam | MR | Zbl

[20] Hamilton, Richard S. Three-manifolds with positive Ricci curvature, J. Differential Geom., Volume 17 (1982) no. 2, pp. 255-306 | MR | Zbl

[21] Hamilton, Richard S. Four-manifolds with positive curvature operator, J. Differential Geom., Volume 24 (1986) no. 2, pp. 153-179 | MR | Zbl

[22] Hamilton, Richard S. The formation of singularities in the Ricci flow, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), Internat. Press, Cambridge, MA, 1995, pp. 7-136 | MR | Zbl

[23] Hamilton, Richard S. Four-manifolds with positive isotropic curvature, Comm. Anal. Geom., Volume 5 (1997) no. 1, pp. 1-92 | MR | Zbl

[24] Hamilton, Richard S. Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom., Volume 7 (1999) no. 4, pp. 695-729 | MR | Zbl

[25] Hempel, John 3-manifolds, Annals of mathematics studies, 086, Princeton University Press, Princeton, 1976 | MR | Zbl

[26] Jaco, William Lectures on three-manifold topology, CBMS Lecture Notes, 43, American Mathematical Society, Providence, Rhode Island, USA, 1980 | MR | Zbl

[27] Jaco, William H.; Shalen, Peter B. Seifert fibered spaces in 3-manifolds, Memoirs of the American Mathematical Society, American Mathematical Society, Providence, Rhode Island, USA, 1979 no. 220 | MR

[28] Johannson, Klaus Homotopy equivalences of 3-manifolds with boundary, Lecture Notes in Mathematics, 761, Springer, Berlin, 1979 | MR | Zbl

[29] Kapovich, Michael Hyperbolic manifolds and discrete groups, Progress in Mathematics, 183, Birkhäuser Boston Inc., Boston, MA, 2001 | MR | Zbl

[30] Kleiner, Bruce; Lott, John Notes on Perelman’s papers, ArXiv: math.DG/0605667, 2006

[31] Lott, John On the long-time behavior of type-III Ricci flow solutions, Math. Ann., Volume 339 (2007) no. 3, pp. 627-666 | MR

[32] Maillot, Sylvain Open 3-manifolds whose fundamental groups have infinite center, and a torus theorem for 3-orbifolds, Trans. Amer. Math. Soc., Volume 355 (2003) no. 11, p. 4595-4638 (electronic) | MR | Zbl

[33] Mess, Geoffrey The Seifert conjecture and groups which are coarse quasiisometric to planes (Preprint)

[34] Morgan, John; Tian, Gang Ricci flow and the Poincaré conjecture, Clay Mathematics Monographs, 3, American Mathematical Society, Providence, RI, 2007 | MR

[35] Myers, Robert Simple knots in compact, orientable 3-manifolds, Trans. Amer. Math. Soc., Volume 273 (1982) no. 1, pp. 75-91 | MR | Zbl

[36] Otal, Jean-Pierre Thurston’s hyperbolization of Haken manifolds, Surveys in differential geometry, Vol. III (Cambridge, MA, 1996), Int. Press, Boston, MA, 1998, pp. 77-194 | Zbl

[37] Otal, Jean-Pierre The hyperbolization theorem for fibered 3-manifolds, SMF/AMS Texts and Monographs, 7, American Mathematical Society, Providence, RI, 2001 (Translated from the 1996 French original by Leslie D. Kay) | MR | Zbl

[38] Pansu, P. Effondrement des variétés riemanniennes, d’après J. Cheeger et M. Gromov, Astérisque, Volume 121-122 (1985), pp. 63-82 (Seminar Bourbaki, Vol. 1983/84) | Numdam | Zbl

[39] Perelman, Grisha The entropy formula for the Ricci flow and its geometric applications, ArXiv : math.DG/0211159, 2002 | Zbl

[40] Perelman, Grisha Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, ArXiv : math.DG/0307245, 2003 | Zbl

[41] Perelman, Grisha Ricci flow with surgery on three-manifolds, ArXiv : math.DG/0303109, 2003 | Zbl

[42] Schoen, Richard; Yau, Shing-Tung Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2), Volume 110 (1979) no. 1, pp. 127-142 | MR | Zbl

[43] Scott, Peter The geometries of 3-manifolds, Bull. London Math. Soc., Volume 15 (1983), pp. 401-487 | MR | Zbl

[44] Scott, Peter There are no fake Seifert fibered spaces with infinite π 1 , Annals of Math., Volume 117 (1983), pp. 35-70 | MR | Zbl

[45] Shioya, Takashi; Yamaguchi, Takao Volume collapsed three-manifolds with a lower curvature bound, Math. Ann., Volume 333 (2005) no. 1, pp. 131-155 | MR | Zbl

[46] Soma, Teruhiko The Gromov invariant of links, Invent. Math., Volume 64 (1981) no. 3, pp. 445-454 | MR | Zbl

[47] Tukia, Pekka Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math., Volume 391 (1988), pp. 1-54 | MR | Zbl

[48] Waldhausen, Friedhelm Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II, Invent. Math. 3 (1967), 308–333; ibid., Volume 4 (1967), pp. 87-117 | MR | Zbl

Cited by Sources: