Raoul Bott

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Raoul Bott (photography 1986)

Raoul Bott (* 24. September 1923 in Budapest ; † 20th December 2005 in Carlsbad , California ) was a US -American mathematician , known for his many contributions to topology and geometry became known.

Life

Bott lived much of his life in the United States. His mother and aunt spoke Hungarian. Since his Czech stepfather was German-speaking, he grew up with the German language . He learned English from an early age and spoke it perfectly except for a small accent. He went to school in Slovakia and thus also learned Slovak . Despite these circumstances, Bott always claimed that he had an aversion to language learning.

In 1938 he fled with his stepparents via England to Canada , where he entered McGill University in Montréal and initially studied electrical engineering . Bott began his work in the theory of electrical lines ( Bott-Duffin theorem from 1949), but then switched to pure mathematics . In 1949 he received his doctorate from the Carnegie Institute of Technology with Richard Duffin ( Electrical Network Theory ). He then worked at the Institute of Advanced Studies and the University of Michigan. In 1956 he became a Sloan Research Fellow .

From 1959 to 1999 Bott was a professor at Harvard University, where he held the prestigious "William Caspar Graustein Professorship for Mathematics". In 1959 he was elected to the American Academy of Arts and Sciences , in 1964 to the National Academy of Sciences . In 2000 he received the Wolf Prize . In 1980 he was elected a member of the Leopoldina , in 2005 he became an external member of the Royal Society of London .

He studied the homotopy groups of Lie groups using the methods of Morse code theory . This led to Bott's periodicity theorem in 1959. In this work he introduced the Morse-Bott functions , which represent an important generalization of the Morse functions. This led to his longstanding collaboration with Michael Atiyah , originally brought about by the contribution he made in the periodicity of K-theory . He made significant contributions to the index theorem , especially in the formulation of the related fixed-point theorem , the so-called Woods Hole fixed-point theorem ( Atiyah-Bott fixed-point theorem ), a combination of the Riemann-Roch theorem and the Lefschetz fixed-point theorem , which is based on Woods Hole , Massachusetts (home of a molecular biology research institute and well-known conference venue).

Bott also became known for the connection of the Borel-Bott-Weil theorem to the representation theory of Lie groups using holomorphic sheaves and their cohomology groups , as well as for his work on foliage .

Bott died of complications from cancer.

His PhD students include Fields medalists Stephen Smale and Daniel Quillen, as well as Peter Landweber , Robert MacPherson and Constantin Teleman .

Honourings and prices

See also

literature

  • S.-T. Yau (Ed.): The founders of index theory: reminiscences of Atiyah, Bott, Hirzebruch and Singer, International Press, Somerville 2003

Fonts

  • with Loring W. Tu Differential forms in algebraic topology . Springer, 1982
  • Collected papers . 4 volumes. Birkhäuser, 1994/95
  • Lectures on K (X) . Benjamin, 1969
  • On topological obstructions to integrability . ICM 1970, Nice
  • with Mather Topics in topology and differential geometry . In: Batelle Rencontres , 1967 (de Witt, Wheeler ed.)
  • The periodicity theorem for the classical groups and some of its applications . In: Advances in Mathematics , Volume 4, 1970, pp. 353-411
  • Vector fields on spheres . In: L'enseignment mathematique , Volume 7, 1961, pp. 125-138
  • On the shape of a curve . In: Advances in Mathematics , Volume 16, 1975, pp. 144-159
  • Morse Theory indomitable . In: Publ.Math.IHES , Volume 68, 1988, p. 99, Numdam
  • Lectures on Morse theory, old and new . In: Bull. Amer. Math. Soc. , Volume 7, 1982, p. 331
  • Homogeneous vector bundles . In: Annals of Mathematics , 66, 1957, pp. 933-935 ( Borel-Weil-Bott theorem : Construction of representations of Lie groups using sheaf cohomology)
  • The stable homotopy of the classical groups . In: Annals of Mathematics , 70, 1959, pp. 313-337. ( Bott periodicity theorem for stable homotopy groups of Lie groups)
  • On a topological obstruction to integrability . In: Global Analysis, Proceedings of Symposia in Pure Math. , XVI, 1970, pp. 127-131 (integrability of sub-bundles via Pontryagin classes )
  • with Atiyah On the periodicity theorem for complex vector bundles . In: Acta Mathematica , Volume 112, 1964, pp. 229-247
  • with Atiyah A Lefschetz Fixed-point Formula for Elliptic Complexes , Part 1,2. In: Annals of Mathematics , Volume 86, 1967, pp. 374-407, Volume 88, 1968, pp. 451-491
  • with Atiyah, Shapiro: Clifford Modules . In: Topology , Vol. 3, Suppl. 1, 1964, pp. 3-38
  • with Atiyah: The Yang-Mills equations over Riemann surfaces . In: Phil. Trans. R. Soc. Lond. , A, 308, 1982, pp. 524-615 (equivariant Morse theory)
  • with Atiyah: The moment map and equivariant cohomology . In: Topology , 23, 1984, pp. 1–28 (localization formula for equivariant cohomology )

Web links

Individual evidence

  1. ↑ nytimes.com
  2. ↑ boston.com
  3. ^ Mathematics Genealogy Project
personal data
SURNAME Bott, Raoul
BRIEF DESCRIPTION Hungarian-American mathematician
DATE OF BIRTH September 24, 1923
PLACE OF BIRTH Budapest
DATE OF DEATH December 20, 2005
Place of death Carlsbad (California)