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Raoul Bott

Raoul Bott in 1986
Born September 24, 1923(1923-09-24)
Budapest, Hungary
Died December 20, 2005 (aged 82)
San Diego, California
Residence Slovakia
United States
Institutions University of Michigan in Ann Arbor
Harvard University
Alma mater McGill University
Carnegie Mellon University
Doctoral advisor Richard Duffin
Doctoral students Harold Edwards
Robert MacPherson
Daniel Quillen
Stephen Smale
Notable awards Oswald Veblen Prize in Geometry (1964)
Wolf Prize (2000)

Raoul Bott, FRS (September 24, 1923 – December 20, 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.



Bott was born in Budapest, Hungary, grew up in Slovakia and spent his working life in the United States. His family emigrated to Canada in 1938, and subsequently he served in the Canadian Army in Europe during World War II. He later went to college at McGill University in Montreal, and then earned a Ph.D. from Carnegie Mellon University in Pittsburgh in 1949. His thesis, titled Electrical Network Theory, was written under the direction of Richard Duffin. Afterward, he began teaching at the University of Michigan in Ann Arbor. He was a professor at Harvard University from 1959 to 1999, and received the Wolf Prize in 2000. In 2005, he was elected an Overseas Fellow of the Royal Society of London. He died in San Diego after a battle with cancer.

Initially he worked on the theory of electrical circuits (Bott-Duffin theorem from 1949), then switched to pure mathematics.

He studied the homotopy theory of Lie groups, using methods from Morse theory, leading to the Bott periodicity theorem (1956). In the course of this work, he introduced Morse–Bott functions, an important generalization of Morse functions.

This led to his role as collaborator over many years with Michael Atiyah, initially via the part played by periodicity in K-theory. Bott made important contributions towards the index theorem, especially in formulating related fixed-point theorems, in particular the so-called 'Woods Hole fixed-point theorem', a combination of the Riemann–Roch theorem and Lefschetz fixed-point theorem (it is named after Woods Hole, Massachusetts, the site of a conference at which collective discussion formulated it).[1] The major Atiyah–Bott papers on what is now the Atiyah–Bott fixed-point theorem were written in the years up to 1968; they collaborated further in recovering in contemporary language results of Ivan Petrovsky on hyperbolic partial differential equations, prompted by Lars Gårding. In the 1980s, Atiyah and Bott investigated gauge theory, using the Yang–Mills equations on a Riemann surface to obtain topological information about the moduli spaces of stable bundles on Riemann surfaces.

He is also well-known in connection with the Borel–Bott–Weil theorem on representation theory of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations.


In 1964, he was awarded the Oswald Veblen Prize in Geometry by the American Mathematical Society. In 1983 he was awarded the Jeffery–Williams Prize by the Canadian Mathematical Society.


Bott had 20 Ph.D. students, including Stephen Smale, Lawrence Conlon, Daniel Quillen, Peter Landweber, Robert MacPherson, Robert Brooks, Robin Forman and Kevin Corlette.




His mother and aunts spoke Hungarian. His Czech stepfather did not, so the principal language at home was German. He had an English governess from a young age, so he also spoke perfect English (and retained a very faint English accent throughout his life). The language of his high school was Slovak. Despite all this Bott claimed a distaste for learning languages.


  • Bott, Raoul Raoul Bott: collected papers. Vol. 4. Mathematics related to physics. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1995. xx+485 pp. ISBN 0-8176-3648-X MR1321890
  • Bott, Raoul Raoul Bott: collected papers. Vol. 3. Foliations. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1995. xxxii+610 pp. ISBN 0-8176-3647-1 MR1321886
  • Bott, Raoul Raoul Bott: collected papers. Vol. 2. Differential operators. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1994. xxxiv+802 pp. ISBN 0-8176-3646-3MR1290361
  • Bott, Raoul Raoul Bott: collected papers. Vol. 1. Topology and Lie groups. Edited by Robert D. MacPherson. Contemporary Mathematicians. Birkhäuser Boston, Inc., Boston, MA, 1994. xii+584 pp. ISBN 0-8176-3613-7 MR1280032
  • Bott, Raoul; Tu, Loring W. Differential forms in algebraic topology. Graduate Texts in Mathematics, 82. Springer-Verlag, New York-Berlin, 1982. xiv+331 pp. ISBN 0-387-90613-4 MR0658304
  • Bott, Raoul Lectures on K(X). Mathematics Lecture Note Series W. A. Benjamin, Inc., New York-Amsterdam 1969 x+203 pp.MR0258020


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