Dennis Sullivan

Dennis Parnell Sullivan ( born February 12, 1941 in Port Huron, Michigan ) is an American mathematician who deals with topology and dynamical systems.

Sullivan was born in 1966 at Princeton University with William Browder PhD ( Triangulating homotopy equivalences ). He then entered Princeton, the Massachusetts Institute of Technology (MIT) and over 20 years as a member of the IHES in Paris and is currently a professor at Stony Brook University and has the Albert Einstein Chair at the Graduate Center ( Graduate Center ) of the City University of New York ( CUNY ) holds.

Sullivan is with Browder, Sergei Petrovich Novikov and Wall CTC one of the founders of Surgery Theory (surgery ) the fragmentation of topological manifolds. He founded a geometric access to homotopy theory, based on its localization principle, and with Daniel Quillen rational homotopy theory, based on the theory of differential forms.

To 1967, he and Andrew Casson refuted the " main conjecture " ( Steinitz and Heinrich Tietze, 1908), which claimed the unique Triangulierbarkeit triangulable of topological manifolds. They found an obstruction in higher ( five or more ) dimensions. For up to three dimensions, however, it is correct ( shown by Edward M. Brown 1963). A first counterexample in dimension 8 was previously 1961 John Milnor.

In dynamical systems theory, he proved for the iteration of holomorphic images of the Riemann sphere 1985, the No- Wandering Theorem ( Quasiconformal homeomorphisms and dynamics Annals of Mathematics, Bd.122, S.408. ): Every connected component of the Fatou set ( the complement the Julia set ) of the iteration of a rational illustration of second degree or higher is periodic.

The Sullivan conjecture states that the space of the images of Klassifzierungsraums of a finite group on a finite CW - complex is weak kontraktibel ( that is, all homotopy groups are trivial ). It was proved by Haynes Miller.

In 1999 he founded with Moira Chas String Topology based on the observation of arrays of loops ( loops) based on manifolds for which a multiplication is defined.

In 1971 he was awarded the Oswald Veblen Prize - 1981 to Elie Cartan Prize in Geometry, 1994 King Faisal Prize, the 2004 National Medal of Science, and in 2006 he received Leroy P. Steele Prize. In 2010 he received the Wolf Prize. 1970 in Nice ( Galois symmetry in manifold theory at the primes ) and 1974 in Vancouver, he was invited speaker ( plenary lecture ) at the International Congress of Mathematicians (ICM ) ( Inside and Outside manifolds ). He is a Fellow of the American Mathematical Society.

His doctoral counts Curtis McMullen.

Writings

  • With Pierre Deligne, Phillip Griffiths and John Morgan: Real homotopy theory of Kähler manifolds. In: Inventiones Mathematicae. Vol 29, No. 3, 1975, ISSN 0020-9910, pp. 245-274, online ( PDF, 1.57 MB).
  • Cycles for the dynamical study of foliated manifolds and complex manifolds. In: Inventiones Mathematicae. Vol 36, 1976, p 225-255, online ( PDF, 1.63 MB).
  • Infinitesimal computations in topology. In: Institut des Hautes Études Scientifiques. Publications Mathématiques. Vol 47, No 1, December 1977, ISSN 0073-8301, pp. 269-331.
  • The density at infinity of a discrete group of hyperbolic motions. In: Institut des Hautes Études Scientifiques. Publications Mathématiques. Vol 50 (1979 ), 171-202, online ( PDF, 3.1 MB).
  • On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions. In: Irwin Kra, Bernard Maskit (ed.): Riemann surfaces and related topics. Proceedings of the 1978 Stony Brook Conference ( = Annals of Mathematics Studies. Vol. 97). Princeton University Press, Princeton NJ 1981, ISBN 0-691-08264-2, pp. 465-496.
  • With Ricardo Mañé, Paulo Sad: On the dynamics of rational maps. In: Annales Scientifiques de l' École Normale Supérieure. Série 4, Vol 16, No. 2, 1983, ISSN 0012-9593, pp. 193-217. online ( PDF, 2.68 MB).
  • Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups. In: Acta Mathematica. Vol 153, No 1, 1984 ISSN 0001-5962, pp. 259-277, online ( PDF, 780 KB).
  • Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou - Julia Problem on Wandering Domains. In: Annals of Mathematics. Series 2, Vol 122, No. 2, 1985 ISSN 0003- 486x, pp. 401-418; II: Structural Stability Implies Hyperbolicity for Kleinian groups. In: Acta Mathematica. Vol 155, No. 1, 1985, pp. 243-260, online ( PDF, 859 KB ); III: with Curtis McMullen: The Teichmüller space of a holomorphic dynamical system. In: Advances in Mathematics. Vol 135, No. 2, 1998 ISSN 0001-8708, pp. 351-395, online ( PDF, 360 KB).
  • Geometric topology Localization, periodicity and Galois symmetry. The 1970 MIT notes ( = K- Monographs in Mathematics. Vol. 8). Edited and with a preface by Andrew Ranicki. Springer, Dordrecht 2005, ISBN 1-4020-3511- X.
  • Moira Chas: String Topology. 2008, ArXiv.
Mathematical Sciences Research Institute William Browder (mathematician) Institut des Hautes Études Scientifiques Sergei Novikov (mathematician) C. T. C. Wall Heinrich Franz Friedrich Tietze Oswald Veblen Prize in Geometry Curtis T. McMullen John Morgan (mathematician) Carl Ludwig Siegel Jean Leray Henri Cartan Oscar Zariski Hassler Whitney Mark Krein Kunihiko Kodaira Hans Lewy Samuel Eilenberg Atle Selberg Ennio de Giorgi Ilya Piatetski-Shapiro Lennart Carleson Mikhail Leonidovich Gromov Jacques Tits Joseph Keller Yakov Sinai Raoul Bott Jean-Pierre Serre John Tate Stephen Smale David Mumford Luis Caffarelli Michael Artin
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