Geometrization of three-dimensional orbifolds via Ricci flow
Local collapsing, orbifolds, and geometrization, Astérisque, no. 365 (2014), pp. 101-177.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez le site de la revue.
@incollection{AST_2014__365__101_0,
     author = {Kleiner, Bruce and Lott, John},
     title = {Geometrization of three-dimensional orbifolds via {Ricci} flow},
     booktitle = {Local collapsing, orbifolds, and geometrization},
     series = {Ast\'erisque},
     pages = {101--177},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {365},
     year = {2014},
     mrnumber = {3244330},
     language = {en},
     url = {http://www.numdam.org/item/AST_2014__365__101_0/}
}
TY  - CHAP
AU  - Kleiner, Bruce
AU  - Lott, John
TI  - Geometrization of three-dimensional orbifolds via Ricci flow
BT  - Local collapsing, orbifolds, and geometrization
AU  - Collectif
T3  - Astérisque
PY  - 2014
SP  - 101
EP  - 177
IS  - 365
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2014__365__101_0/
LA  - en
ID  - AST_2014__365__101_0
ER  - 
%0 Book Section
%A Kleiner, Bruce
%A Lott, John
%T Geometrization of three-dimensional orbifolds via Ricci flow
%B Local collapsing, orbifolds, and geometrization
%A Collectif
%S Astérisque
%D 2014
%P 101-177
%N 365
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2014__365__101_0/
%G en
%F AST_2014__365__101_0
Kleiner, Bruce; Lott, John. Geometrization of three-dimensional orbifolds via Ricci flow, dans Local collapsing, orbifolds, and geometrization, Astérisque, no. 365 (2014), pp. 101-177. http://www.numdam.org/item/AST_2014__365__101_0/

[1] A. Adem, J. Leida & Y. Ruan - Orbifolds and stringy topology, Cambridge Tracts in Math. vol. 171, Cambridge Univ. Press, Cambridge, 2007. | MR | Zbl

[2] M. T. Anderson - "Scalar curvature and the existence of geometric structures on 3-manifolds. I", J. Reine Angew. Math. 553 (2002), p. 125-182. | MR | Zbl

[3] A. L. Besse - Einstein manifolds, Ergeb. Math. Grenzgeb. (3), vol. 10, Springer-Verlag, Berlin, 1987. | MR | Zbl

[4] M. Boileau, B. Leeb & J. Porti - "Geometrization of 3-dimensional orbifolds", Ann. of Math. (2) 162 (2005), no. 1, p. 195-290. | DOI | MR | Zbl

[5] M. Boileau, S. Maillot & J. Porti - Three-dimensional orbifolds and their geometric structures, Panoramas & Synthèses, vol. 15, Soc. Math. France, Paris, 2003. | MR | Zbl

[6] M. Boileau & J. Porti "Geometrization of 3-orbifolds of cyclic type", Astérisque (2001), no. 272, p. 208. | Numdam | MR | Zbl

[7] F. Bonahon & L. Siebenmann - "The classification of Seifert fibred 3-orbifolds", in Low-dimensional topology (Chelwood Gate, 1982), London Math. Soc. Lecture Note Ser., vol. 95, Cambridge Univ. Press, Cambridge, 1985, p. 19-85. | DOI | MR | Zbl

[8] J. E. Borzellino - "Riemannian geometry of orbifolds", Ph.D. Thesis, University of California, Los Angeles, 1992, http://www.calpoly.edu/~jborzell/Publications/Publication%20PDFs/phd_thesis.pdf. | MR

[9] J. E. Borzellino, "Orbifolds of maximal diameter", Indiana Univ. Math. J. 42 (1993), no. 1, p. 37-53. | DOI | MR | Zbl

[10] J. E. Borzellino & S.-H. Zhu - "The splitting theorem for orbifolds", Illinois J. Math. 38 (1994), no. 4, p. 679-691. | MR | Zbl

[11] G. E. Bredon - Introduction to compact transformation groups, Pure Applied Math., vol. 46, Academic Press, New York-London, 1972. | MR | Zbl

[12] M. R. Bridson & A. Haefliger - Metric spaces of non-positive curvature, Grundlehren Math. Wiss., vol. 319, Springer-Verlag, Berlin, 1999. | MR | Zbl

[13] D. Burago, Y. Burago & S. Ivanov - A course in metric geometry, Grad. Stud. Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001. | DOI | MR | Zbl

[14] J. Cheeger - "Critical points of distance functions and applications to geometry", in Geometric topology: recent developments (Montecatini Terme, 1990), Lecture Notes in Math., vol. 1504, Springer, Berlin, 1991, p. 1-38. | MR | Zbl

[15] J. Cheeger, K. Fukaya & M. Gromov - "Nilpotent structures and invariant metrics on collapsed manifolds", J. Amer. Math. Soc. 5 (1992), no. 2, p. 327-372. | DOI | MR | Zbl

[16] J. Cheeger & D. Gromoll - "The splitting theorem for manifolds of nonnegative Ricci curvature", J. Differential Geom. 6 (1971/72), p. 119-128. | DOI | MR | Zbl

[17] J. Cheeger & D. Gromoll, "On the structure of complete manifolds of nonnegative curvature", Ann. of Math. (2) 96 (1972), p. 413-443. | DOI | MR | Zbl

[18] B. Chow, S.-C. Chu, D. Glickenstein, C. Guenther, J. Isenberg, T. Ivey, D. Knopf, P. Lu, F. Luo & L. Ni - The Ricci flow: techniques and applications. Part I: Geometric aspects, Math. Surveys Monogr., vol. 135, Amer. Math. Soc., Providence, RI, 2007. | MR | Zbl

[19] D. Cooper, C. D. Hodgson & S. P. Kerckhoff - Three-dimensional orbifolds and cone-manifolds, MSJ Mem., vol. 5, Math. Soc Japan, Tokyo, 2000. | MR | Zbl

[20] D. M. Deturck - "Deforming metrics in the direction of their Ricci tensors", J. Differential Geom. 18 (1983), no. 1, p. 157-162. | DOI | MR | Zbl

[21] J. Dinkelbach & B. Leeb - "Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds", Geom. Topol. 13 (2009), no. 2, p. 1129-1173. | DOI | MR | Zbl

[22] W. D. Dunbar - "Geometric orbifolds", Rev. Mat. Univ. Complut. Madrid 1 (1988), no. 1-3, p. 67-99. | EuDML | MR | Zbl

[23] W. D. Dunbar, "Nonfibering spherical 3-orbifolds", Trans. Amer. Math. Soc. 341 (1994), no. 1, p. 121-142. | MR | Zbl

[24] D. Faessler - "On the Topology of Locally Volume Collapsed Riemannian 3-Orbifolds", preprint, http://arxiv.org/abs/1101.3644, 2011. | Zbl

[25] B. Farb & D. Margalit - A primer on mapping class groups, Princeton Math. Ser., vol. 49, Princeton Univ. Press, Princeton, NJ, 2012. | MR

[26] K. Fukaya - "A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters", J. Differential Geom. 28 (1988), no. 1, p. 1-21. | DOI | MR | Zbl

[27] D. Gromoll & G. Walschap - Metric foliations and curvature, Progr. Math., vol. 268, Birkhäuser Verlag, Basel, 2009. | MR | Zbl

[28] K. Grove & K. Shiohama - "A generalized sphere theorem", Ann. of Math. (2) 106 (1977), no. 2, p. 201-211. | DOI | MR | Zbl

[29] A. Haefliger - "Orbi-espaces", in Sur les groupes hyperboliques d'après Mikhael Gromov (E. Ghys & P. de la Harpe, eds.), Progr. Math., vol. 83, Birkhauser Boston, Inc., Boston, MA, 1990, p. 203-213. | DOI | MR

[30] R. S. Hamilton - "Three-manifolds with positive Ricci curvature", J. Differential Geom. 17 (1982), no. 2, p. 255-306. | DOI | MR | Zbl

[31] R. S. Hamilton, "Four-manifolds with positive curvature operator", J. Differential Geom. 24 (1986), no. 2, p. 153-179. | DOI | MR | Zbl

[32] R. S. Hamilton, "A compactness property for solutions of the Ricci flow", Amer. J. Math. 117 (1995), no. 3, p. 545-572. | DOI | MR | Zbl

[33] R. S. Hamilton, "Non-singular solutions of the Ricci flow on three-manifolds", Comm. Anal. Geom. 7 (1999), no. 4, p. 695-729. | DOI | MR | Zbl

[34] R. S. Hamilton, "Three-orbifolds with positive Ricci curvature", in Collected papers on Ricci flow, Ser. Geom. Topol., vol. 37, Int. Press, Somerville, MA, 2003, p. 521-524. | MR

[35] C. Hog-Angeloni & S. Matveev - "Roots in 3-manifold topology", in The Zieschang Gedenkschrift, Geom. Topol. Monogr., vol. 14, Geom. Topol. Publ., Coventry, 2008, p. 295-319. | DOI | MR | Zbl

[36] M. Kapovich - Hyperbolic manifolds and discrete groups, Progress in Mathematics, vol. 183, Birkhäuser Boston, Inc., Boston, MA, 2001. | MR | Zbl

[37] B. Kleiner & J. Lott - "Locally collapsed 3-manifolds", in this volume. | Numdam

[38] B. Kleiner & J. Lott,"Notes on Perelman's papers", Geom. Topol. 12 (2008), no. 5, p. 2587-2855. | DOI | MR | Zbl

[39] S. Kobayashi & K. Nomizu - Foundations of differential geometry. Vol I, Interscience Publishers, New York, 1963. | MR | Zbl

[40] P. Lu - "A compactness property for solutions of the Ricci flow on orbifolds", Amer. J. Math. 123 (2001), no. 6, p. 1103-1134. | DOI | MR | Zbl

[41] C. Mcmullen - "Iteration on Teichmüller space", Invent. Math. 99 (1990), no. 2, p. 425-454. | DOI | EuDML | MR | Zbl

[42] W. H. Meeks, Iii &Amp; S. T. Yau - "The classical Plateau problem and the topology of three-dimensional manifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's lemma", Topology 21 (1982), no. 4, p. 409-442. | DOI | MR | Zbl

[43] W. H. Meeks, Iii &Amp; S. T. Yau,"The existence of embedded minimal surfaces and the problem of uniqueness", Math. Z. 179 (1982), no. 2, p. 151-168. | DOI | EuDML | MR | Zbl

[44] I. Moerdijk - "Orbifolds as groupoids: an introduction", in Orbifolds in mathematics and physics (Madison, WI, 2001), Contemp. Math., vol. 310, Amer. Math. Soc., Providence, RI, 2002, p. 205-222. | DOI | MR | Zbl

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

[46] L. Ni & N. Wallach - "On a classification of gradient shrinking solitons", Math. Res. Lett. 15 (2008), no. 5, p. 941-955. | DOI | MR | Zbl

[47] J.-P. Otal - "Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3", Astérisque (1996), no. 235, p. x+159. | Numdam | MR | Zbl

[48] J.-P. Otal,"Thurston's hyperbolization of Haken manifolds", in Surveys in differential geometry. Vol. III (Cambridge, MA, 1996), Int. Press, Boston, MA, 1998, p. 77-194. | MR | Zbl

[49] G. Perelman - "The Entropy Formula for the Ricci Flow and its Geometric Applications", preprint, http://arXiv.org/abs/math.DG/0211159, 2002. | Zbl

[50] G. Perelman,"Ricci Flow with Surgery on Three-Manifolds", preprint, http://arxiv.org/abs/math.DG/0303109, 2003. | Zbl

[51] J. Petean & G. Yun - "Surgery and the Yamabe invariant", Geom. Fund. Anal. 9 (1999), no. 6, p. 1189-1199. | DOI | MR | Zbl

[52] P. Petersen & W. Wylie - "On the classification of gradient Ricci solitons", Geom. Topol. 14 (2010), no. 4, p. 2277-2300. | DOI | MR | Zbl

[53] C. Petronio - "Spherical splitting of 3-orbifolds", Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 2, p. 269-287. | DOI | MR | Zbl

[54] P. Scott - "The geometries of 3-manifolds", Bull. London Math. Soc. 15 (1983), no. 5, p. 401-487. | DOI | MR | Zbl

[55] M. E. Taylor - Partial differential equations. III, Appl. Math. Sciences, vol. 117, Springer-Verlag, New York, 1997. | MR | Zbl

[56] W. P. Thurston - "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry", Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, p. 357-381. | DOI | MR | Zbl

[57] W. P. Thurston, "Three-Manifolds with Symmetry", preprint, 1982.

[58] L.-F. Wu - "The Ricci flow on 2-orbifolds with positive curvature", J. Differential Geom. 33 (1991), no. 2, p. 575-596. | DOI | MR | Zbl

[59] R. Ye - "Notes on 2-Dimensional κ-Solutions", http://www.math.ucsb.edu/~yer/kappa-solutions.pdf.