Recent progress on the poincaré conjecture and the classification of 3-manifolds

Bulletin of the American Mathematical Society

Volumn 42, Issue 1, 2005, Pages 57-78

  Morgan, John W ^a  

^a Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13644265984     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-04-01045-6     Document Type: Article

References (26)

1. Y. Burago, M. Gromov and G. Perelman, "A. D. Aleksandrov spaces with curvature bounded below," Russian Math. Surveys 47 (1992), 1-58. MR1185284 (93m:53035)
2. J. Cheegar and M. Gromov, "Collapsing Riemannian manifolds while keeping their curvatures bounded, I, II." J. Differential Geom. 23 (1986), 309-346; 32 (1990), 269-298. MR0852159 (87k:53087); MR1064875 (92a:53066)
3. J. Cheegar and M. Gromov, "Collapsing Riemannian manifolds while keeping their curvatures bounded, I, II." J. Differential Geom. 23 (1986), 309-346; 32 (1990), 269-298. MR0852159 (87k:53087); MR1064875 (92a:53066)
4. T. Colding and W. Minicozzi, "Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman," arXiv.math.DG/0308090, August 25, 2003.
5. D. Cooper, C. Hodgson, S. Kerchoff, 3-dimensional orbifolds and cone-manifolds, Math. Soc. Japan Memoirs, Vol. 5, Tokyo, 2000. MR1778789 (2002c:57027)
6. R. Hamilton, "Three-manifolds with positive Ricci curvature," J. Differential Geom. 17 (1982), 255-306. MR0664497 (84a:53050)
7. R. Hamilton, "The Harnack estimate for the Ricci flow," J. Differential. Geom. 37 (1993), 225-243. MR1198607 (93k:58052)
8. R. Hamilton, "Formation of singularities in the Ricci flow," Surveys in Differential Geometry 2, 7-136, International Press, 1995. MR1375255 (97e:53075)
9. R. Hamilton, "Four-manifolds with positive Isotropic curvature," Comm. Anal. Geom. 5 (1997), 1-92. MR1456308 (99e:53049)
10. R. Hamilton, "Non-singular solutions of the Ricci flow on three-manifolds," Comm. Analysis and Geometry 7 (1999), 695-729. MR1714939 (2000g:53034)
11. J. Hempel, 3-manifolds, Ann. of Math. Studies, Vol. 86, Princeton University Press, 1976. MR0415619 (54:3702)
12. H. Kneser, "Geschlossene Flächen in drei-dimesnionalen Mannigfaltigkeiten," Jahresber. Deutsch. Math. Verbein 38 (1929), 248-260.
13. n without fixed points," Amer. Journal of Math. 79 (1957), 623-630. MR0090056 (19:761d)
14. J. Milnor, "Towards the Poincaré Conjecture and the classification of 3-manifolds," Notices AMS 50 (2003), 1226-1233. MR2009455 (2004h:57022)
15. G. Perelman, "Spaces with curvature bounded below," Proceedings of ICM 1994, 517-525, Birkhäuser, 1995. MR1403952 (97g:53055)
16. G. Perelman, "The entropy formula for the Ricci flow and its geometric applications," arXiv.math.DG/0211159, November 11, 2002.
17. G. Perelman, "Ricci flow with surgery on three-manifolds," arXiv.math.DG/0303109, March 10, 2003.
18. G. Perelman, "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds," arXiv.math.DG/0307245, July 17, 2003.
19. H. Poincaré, "Cinquième complément à l'analysis situs," Rend. Circ. Mat. Palermo 18 (1904), 45-110. (See Oeuvres, Tome VI, Paris, 1953, p. 498.) MR1401792 (98m:01041)
20. H. Poincaré, "Cinquième complément à l'analysis situs," Rend. Circ. Mat. Palermo 18 (1904), 45-110. (See Oeuvres, Tome VI, Paris, 1953, p. 498.) MR1401792 (98m:01041)
21. P. Scott, "The geometries of 3-manifolds," Bull. London Math. Soc. 15 (1983), 401-487. MR0705527 (84m:57009)
22. H. Seifert, "Topologie dreidimensionaler gefaserter Räume," Acta Math. 60 (1933), 147-288.
23. W-X. Shi, "Deforming the metric on complete riemannian manifolds," J. Differential Geom. 30 (1989), 223-301. MR1001277 (901:58202)
24. T. Shioya and T. Yamaguchi, "Collapsing three-manifolds under a lower curvature bound," J. Differential Geom. 56 (2000), 1-66. MR1863020 (2002k:53074)
25. T. Shioya and T. Yamaguchi, "Volume collapsed three-manifolds with a lower curvature bound," arXiv.math.DG/0304472, April 15, 2003.
26. W. Thurston, Three-dimensional Geometry and Topology, Vol. 1 (Silvio Levy, ed.) Princeton Math. Ser., vol. 35, Princeton Univ. Press, 1997. MR1435975 (97m:57016)