Dennis Sullivan

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Dennis Sullivan at MSRI , 2007

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

Sullivan received his doctorate in 1966 from Princeton University under William Browder ( Triangulating homotopy equivalences ). After that he was in Princeton, at the Massachusetts Institute of Technology (MIT) and for over 20 years a member of IHES near Paris and is currently a professor at Stony Brook University and holds the Albert Einstein Chair at the Graduate Center of the City University of New York (CUNY) inside.

Sullivan, along with Browder, Sergei Petrowitsch Novikow and CTC Wall, is one of the founders of the surgery theory of the division of topological manifolds. He established a geometric approach to homotopy theory , based on his localization principle , and with Daniel Quillen the rational homotopy theory , based on the theory of differential forms .

Around 1967 he and Andrew Casson refuted the “ main conjecture ” (von Steinitz and Heinrich Tietze , 1908), which asserted the unambiguous triangulability (apart from subdivision) of triangulable topological manifolds. They found an obstruction in higher (five and more) dimensions. For up to three dimensions, however, it is correct (shown by Edward M. Brown 1963). A first counterexample in dimension 8 was found by John Milnor in 1961 .

In the theory of dynamic systems he proved the no-wandering theorem ( Quasiconformal homeomorphisms and dynamics. Annals of Mathematics, vol. 122, p. 408) for the iteration of rational mappings of the Riemann sphere in 1985 : every connected component of the Fatou set (the complement of the Julia set ) of the iteration of a rational mapping of degree 2 or higher is periodic. In iteration with transcendent functions, however, there are wandering areas .

The Sullivan conjecture says that the space of the mappings of the classifying space of a finite group to a finite CW-complex is weakly contractible (that is, all homotopy groups are trivial). It was proven by Haynes Miller .

In 1999 he and Moira Chas founded the string topology , which is based on the consideration of cycles in the free loop space of manifolds for which a multiplication is defined.

In 1971 he received the Oswald Veblen Prize , the Elie Cartan Prize in Geometry in 1981, the King Faisal Prize in 1994, the National Medal of Science in 2004 , and the Leroy P. Steele Prize in 2006 . In 2010 he received the Wolf Prize and in 2014 the Balzan Prize . In 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 ; in 1983 he was elected to the National Academy of Sciences , and in 1991 to the American Academy of Arts and Sciences . He has been an honorary member of the Royal Irish Academy since 2011 .

Curtis McMullen is one of his PhD students .

Fonts

  • 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, pp. 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 (Eds.): 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. Series 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 .
  • with Moira Chas: String Topology. 2008, ArXiv .

Web links

Individual evidence

  1. Dennis Sullivan in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. Members: Dennis Parnell Sullivan. Royal Irish Academy, accessed May 13, 2019 .