# Raoul Bott

**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

- In 1958 he was invited speaker at the International Congress of Mathematicians in Edinburgh (An application of Morse theory to the topology of Lie groups)
- 1964 Oswald Veblen Prize
- 1970 Plenary lecture at the ICM Nice (On topological obstructions to integrability)
- 1987 National Medal of Science of the USA
- 1990 Leroy P. Steele Prize from the American Mathematical Society
- 2000 Wolf Prize

## 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

- Literature by and about Raoul Bott in the catalog of the German National Library
- Website about Raoul Bott. Harvard University
*Bott Wins Israel's Wolf Foundation Prize in Mathematics*.-
*Raoul Bott, an Innovator in Mathematics, Dies at 82*. In:*NY Times*, Jan. 8, 2006 - Tu describes Bott's work and biography
- Bott:
*The topological constraints on analysis*. In: AMS history, Volume 2, 1989 - Entry to
*Bott; Raoul (1923–2005)*in the Archives of the*Royal Society*, London - List of publications
- Loring W. Tu (Ed.)
*Remembering Raoul Bott (1923-2005)*, Notices AMS, 2013, No. 4 - numdam.org - some works by Bott (e.g. on Morse code)

## Individual evidence

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) |