Grigorij Perelman, hipoteza Poincar'ego i odrzucony medal Fieldsa

• Autorzy: Przytycki J.H.
• Języki publikacji: PL

Abstrakty

PL

W listopadzie 2002 roku świat matematyczny obiegła wiadomość, że rosyjski matematyk Grigorij Perelman zaanonsował rozwiazanie jednego z najsłynniejszych problemów matematycznych – hipotezy Poincar'ego. Kim jest Perelman? Co i w jaki sposób właściwie udowodnił? Odpowiedzi na te pytania oraz historię otrzymania i odrzucenia medalu Fieldsa w 2006 roku naszkicujemy w tym artykule.

Słowa kluczowe

PL

Perelman Grigorij; biografia naukowa; hipoteza Poincarégo

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2010
• Tom: T. 46, Nr 1
• Strony: 37--61
• Opis fizyczny: Bibliogr. 80 poz., fot.

Twórcy

autor

Przytycki J.H.

• The George Washington University,

Bibliografia

• [1] A. D. Alexandrov, Almost everywhere existence of second differentials of convex functions and some properties of convex surfaces connected with it, Leningrad State Univ. Ann. (Uchenye Zapiski) Math. Ser. 6 (1939), 3-35.
• [2] M. T. Anderson, Geometrization of 3-manifolds via the Ricci flow12, Notices Amer. Math. Soc. 51 (2004), no. 2, 184-193.
• [3] H. Asperger, Autistic psychopathy in childhood, in: Die "Autistischen Psychopathen" im Kindesalter, vol. 117, 1944.
• [4] L. Bessieres, G. Besson, M. Boileau, S. Maillot, J. Porti, Weak collapsing and geometrisation of aspherical 3-manifolds, arXiv.org:math/0706.2065 (2007).
• [5] L. Bessieres, G. Besson, M. Boileau, S. Maillot, J. Porti, Geometrisation of 3-manifolds, to appear, available at http://www-fourier.ujf-grenoble. fr/\~besson/.
• [6] G. Besson, Preuve de le conjecture de Poincaré en déformant le métrique par la courbure de Ricci, d'apr`es G. Perl'man', Astérisque 307 (2006).
• [7] M. Boileau, B. Leeb, J. Porti, Geometrization of 3-dimensional orbifolds, Ann. of Math. 162 (2005), no. 1, 195-290.
• [8] Yu. Burago, M. Gromov, G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below, Uspekhi Mat. Nauk 47 (1992), no. 2(284), 3-51, 222; English transl., Russian Math. Surveys 47 (1992), no. 2, 1-58.
• [9] H.-D. Cao, X.-P. Zhu, A complete proof of the Poincaré and geometrization conjectures - application of the Hamilton-Perelman theory of the Ricci flow, Asian J. Math. 10 (2006), no. 2, 165-492.
• [10] J. Carlson, A. Jaffe, A. Wiles (eds.), The Millennium Prize Problems, American Mathematical Society and Clay Mathematics Institute, Providence, RI, 2006.
• [11] K. J. Devlin, The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, Basic Books, 2002.
• [12] W. Dyck, On the "Analysis Situs" of 3-dimensional spaces, Report of the Brot. Assoc. Adv. Sci. (1884).
• [13] M. Gessen, Perfect rigor ; A genius and the mathematical breakthrough of the century, Houghton Mifflin Harcourt, Boston-New York, 2009.
• [14] C. McA. Gordon, 3-dimensional topology up to 1960, History of topology, North-Holland, Amsterdam, 1999, 449-489.
• [15] G. Farmelo, The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom, Basic Books, 2009.
• [16] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255-306.
• [17] R. S. Hamilton, The formation of singularities in the Ricci flow, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), Int. Press, Cambridge, MA, 1995, 7-136.
• [18] R. S. Hamilton, Four-manifolds with positive isotropic curvature, Comm. Anal. Geom. 5 (1997), no. 1, 1-92.
• [19] R. S. Hamilton, Non-singular solutions of the Ricci flow on three-manifolds, Comm. Anal. Geom. 7 (1999), no. 4, 695-729.
• [20] R. S. Hamilton, List w obronie Shing-Tung Yau13, dostepne pod adresem http://doctoryau.com/hamiltonletter.pdf.
• [21] A. Jackson, Conjectures no more? Consensus forming on the proof of the Poincaré and geometrization conjectures, Notices Amer. Math. Soc. 53 (2006), no. 8, 897-901.
• [22] W. Jakobsche, J. H. Przytycki, Topologia 3-wymiarowych rozmaitosci14, Wydawnictwa Uniwersytetu Warszawskiego, 1987.
• [23] V. Kapovitch, Perelman's stability theorem, Surveys in differential geometry. XI, Surv. Differ. Geom., vol. 11, Int. Press, Somerville, MA, 2007, 103-136.
• [24] B. Kleiner, J. Lott, Notes on Perelman's papers, Geom. Topol. 12 (2008), no. 5, 2587-2855.
• [25] J. Lott, The work of Grigory Perelman, ICM, 2006.
• [26] J. Milnor, A unique decomposition theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1-7.
• [27] J. Milnor, Hyperbolic geometry: the first 150 years, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 1, 9-24.
• [28] J. Milnor, Towards the Poincaré conjecture and the classification of 3-manifolds, Notices Amer. Math. Soc. 50 (2003), no. 10, 1226-1233.
• [29] J. Milnor, The Poincaré Conjecture 99 Years Later: A Progress report (2003).
• [30] J. W. Morgan, Recent progress on the Poincaré conjecture and the classification of 3-manifolds, Bull. Amer. Math. Soc. 42 (2005), no. 1, 57-78.
• [31] J. Morgan, G. Tian, Ricci flow and the Poincaré conjecture, Clay Mathematics Monographs, vol. 3, American Mathematical Society, Providence, RI, 2007.
• [32] J. Morgan, G. Tian, Completion of the Proof of the Geometrization Conjecture15 (September 28, 2008), available at http://front.math.ucdavis. edu/0809.4040.
• [33] J. Morgan, G. Tian, Ricci Flow and the Geometrization Conjecture16, in preparation.
• [34] S. Nasar, A Beautiful Mind: A Biography of John Forbes Nash, Jr., A Touchstone Book, Published by Simon & Shuster, 1998.
• [35] S. Nasar, D. Gruber, Manifold Destiny: A legendary problem and the battle over who solved it, New Yorker (August 28 2006).
• [36] D. O'Shea, The Poincaré Conjecture: In search of the shape of the universe (2007).
• [37] G. Perelman, Sedlowyje powierchnosti w ewklidowych prostranstwach, 1990, Awtoref. dis. na soisk. uczen. step. kand. fiz-mat. nauk. (doktorat).
• [38] G. Perelman, The Entropy Formula for the Ricci Flow and its Geometric Applications, arXiv.org:math.DG/0211159 (11.11.2002).
• [39] G. Perelman, Ricci Flow with Surgery on Three-Manifolds, arXiv.org:math.DG/0303109 (10.03.2003).
• [40] G. Perelman, Finite Extinction Time for the Solutions to the Ricci Flow on Certain Three-Manifolds, arXiv.org:math.DG/0307245 (17.07.2003).
• [41] G. Perelman, Elements of Morse theory on Aleksandrov spaces, Algebra i Analiz 5 (1993), no. 1, 232-241; English transl., St. Petersburg Math. J. 5 (1994), no. 1, 205-213.
• [42] G. Perelman, Proof of the soul conjecture of Cheeger and Gromoll, J. Differential Geom. 40 (1994), no. 1, 209-212.
• [43] G. Perelman, Spaces with curvature bounded below, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, 517-525.
• [44] G. Ya. Perelman, A. M. Petrunin, Extremal subsets in Aleksandrov spaces and the generalized Liberman theorem, Algebra i Analiz 5 (1993), no. 1,
• [45] H. Poincaré, Analysis Situs (&12), Journal d'Ecole Polytechnique Normale 1 (1895), 1-121.
• [46] H. Poincaré, First Complément `a l'analysis situs, 1899, in: OEuvres, vol. VI, Gauthier-Villars, Paris, 1953.
• [47] H. Poincaré, Cinqui`eme complément `a l'analysis situs, Rend. Circ. Math. Palermo 18 (1904), 45-110.
• [48] W.-X. Shi, Deforming the metric on complete Riemannian manifolds17, J. Differential Geom. 30 (1989), no. 1, 223-301.
• [49] G. G. Szapiro, Poincaré Prize; the hundred-year quest to solve one of math's greatest puzzles18, A Plume Book, 2007.
• [50] T. Tao, Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective, arXiv.org:math.DG/0610903v1.
• [51] W. P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982), no. 3, 357-381.
• [52] F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II, Invent. Math. 3 (1967), 308-333; ibid. 4 (1967), 87-117.
• [53] M. Weber, Perelman's proof of the Poincare Conjecture19, vol. 13, Indiana University, Department of Mathematics, Alumni Newsletter, Fall 2008.
• [54] Perelman explains proof to famous math mystery20, The Daily Princetonia (17.04.2003), available at http://www.dailyprincetonian.com/2003/04/17/7979/.
• [55] A. Vershik, Kakim ja jewo znal (2003), available at http://www.mathsoc. spb.ru/pantheon/aleksand/vershik.pdf.
• [56] D. Mackenzie, Mathematics World Abuzz Over Possible Poincaré Proof, Science 300 (2003), 417.
• [57] E. Singer, Mathematics: The reluctant celebrity, Nature 427 (29.01.2004), 388-389.
• [58] D. Overbye, Elusive Proof, Elusive Prover: A New Mathematical Mystery21, New York Times (15.08.2006).
• [59] Guardian (16.08.2006, 26.08.2006).
• [60] Daily Telegraph (17.08.2006).
• [61] N. Lobastova, M. Hirst, World's top maths genius jobless and living with mother, Telegraph (20.08.2006).
• [62] Economist (26.08.2006).
• [63] New Scientist (26.08.2006).
• [64] Geniusz wychodzi z cienia, Gazeta Wyborcza (10.11.2006).
• [65] Hipoteza Poincarégo - juz nie hipoteza, Gazeta Wyborcza (29.12.2006).
• [66] Jewish genius of Russian Math., Ria Novosti (2006).
• [67] Prawda 22 (2006).
• [68] D. Mackenzie, Perelman Declines Math's Top Prize; Three Others Honored in Madrid, Science 313 (2006), 1027.
• [69] D. Mackenzie, Breakthrough of the Year: The Poincaré Conjecture - Proved, Science 314 (2006), no. 5807, 1848-1849.
• [70] Rosja 2006 : Raport z transformacji23.
• [71] Al. Buhbinder, Zagadocznaja historija Grigorija Perelmana (2007), available at http://www.inauka.ru/science/article75067/print.html.
• [72] A. Labisko, dostepne pod adresem http://www.lo.szczecinek.pl/matma/grigorijperelman1.htm.
• [73] C. Sormani, The Poincaré Conjecture24, available at http://comet.lehman.cuny.edu/sormani/.
• [74] Mathematics Genealogy Project, available at http://www.genealogy.ams.org/id.php?id=84354.
• [75] Międzynarodowa Olimpiada Matematyczna 198225, dostępne pod adresem http://www.srcf.ucam.org/~jsm28/imo-scores/1982/.
• [76] Międzynarodowa Olimpiada Matematyczna, dostępne pod adresem http: //www.mimuw.edu.pl/OM/mom.html.
• [77] Audycja radiowa, dostępne pod adresem http://www.polskieradio.pl/ nauka/wszechswiat/artykul4213.html.
• [78] The Fields Medal awards ceremony 2006 in Madrid, available at http: //www.youtube.com/watch?v=GRIdk52VPnI\&feature=related.
• [79] Wikipedia: Grigori Perelman26, available at http://en.wikipedia.org/wiki/Grigori\_Perelman.
• [80] Wywiad z L. Fadiejewem27, dostepne pod adresem http://www.polit.ru/science/2006/10/16/kongress.html.