Michel Kervaire

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Michel André Kervaire (born April 26, 1927 in Częstochowa , Poland , † November 19, 2007 in Geneva ) was a Swiss mathematician who mainly dealt with topology ( differential topology , algebraic topology ) and algebra .

Life

He was the son of the French industrialist André Kervaire attended secondary school in France before 1947-1952 at the Zurich Technical Federal Institute studied, where he in 1955 with a thesis Courbure intégrale généralisée et homotopy at Heinz Hopf doctorate was. From 1959 to 1971 he was a professor at the Courant Institute of Mathematical Sciences of New York University and then until his retirement in 1997 at the University of Geneva . In 1962 he became a Sloan Research Fellow .

Kervaire was the first to show the existence of topological manifolds without differentiable structures (with his Kervaire invariant) and calculated with John Milnor the number of different differentiable structures on so-called “exotic spheres”. He also dealt with knot theory in higher dimensions. The Kervaire invariant problem (which asks in which dimensions manifolds with non-vanishing Kervaire invariants exist) is an important problem in topology that many mathematicians have tried and which has not yet been completely solved.

Kervaire was an honorary member of the Swiss Mathematical Society . From 1980 to 2001 he was the editor of their publication, Commentarii Mathematici Helvetici . In addition, from 1978 he was editor of the magazine L´Enseignement Mathématique . In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( Differentiable structures on spheres and homotopy ) and in 1958 in Edinburgh ( Bernoulli numbers, homotopy groups and a theorem of Rokhlin , with John Milnor ). The University of Neuchâtel awarded him an honorary doctorate in 1986.

Eva Bayer-Fluckiger is one of his doctoral students .

literature

  • Shalom Eliahou, Pierre de la Harpe, Jean-Claude Hausmann, Claude Weber: Michel Kervaire 1927--2007 . In: Notices of the American Mathematical Society . tape 55 , no. 8 , 2008, ISSN  0002-9920 , p. 960–961 ( ams.org [PDF; accessed July 2, 2012]).

Fonts (selection)

  • A manifold which does not admit any differentiable structure. Comment. Math. Helv. 34 1960 257-270.
  • with J. Milnor: Groups of homotopy spheres. I. Ann. of Math. (2) 77 1963 504-537.
  • Le théorème de Barden-Mazur-Stallings. Comment. Math. Helv. 40 1965 31-42.
  • Les nouds de dimensions supérieures. Bull. Soc. Math. France 93 1965 225-271.
  • Smooth homology spheres and their fundamental groups. Trans. Amer. Math. Soc. 144 1969 67-72.
  • mit S. Eliahou: Minimal resolutions of some monomial ideals. J. Algebra 129 (1990) no. 1, 1-25.
  • with S. Eliahou: Sumsets in vector spaces over finite fields. J. Number Theory 71 (1998) no. 1, 12-39.

Web links

Individual evidence

  1. ^ Kervaire: A manifold which does not admit any differentiable structure. Commentarii Mathematici Helvetici, Vol. 34, 1960, p. 257.
  2. ↑ Milnor, Kervaire: Groups of homotopy spheres. Annals of Mathematics Vol. 77, 1963, p. 504.
  3. ↑ Les nœuds des dimensions supérieures. Bulletin de la Société Mathématique de France, Vol. 93, 1965, p. 225
  4. ↑ It has been proven (by Michael J. Hopkins , Hill and Douglas Ravenel 2009, among others ) that the invariant can only be non-zero in dimensions 2, 6, 14, 30, 62 and possibly (the last open case) 126. Victor Snaith on the Kervaire invariant problem
personal data
SURNAME Kervaire, Michel
ALTERNATIVE NAMES Kervaire, Michel A .; Kervaire, Michel André (full name)
BRIEF DESCRIPTION Swiss mathematician
DATE OF BIRTH April 26, 1927
PLACE OF BIRTH Czestochowa
DATE OF DEATH November 19, 2007
Place of death Geneva