Raoul Bott
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'''Raoul Bott''', [[Fellow of the Royal Society|FRS]] (born [[September 24]] [[1923]], died [[December 20]] [[2005]]) was a [[mathematician]] known for numerous basic contributions to [[geometry]] in its broad sense.
He was born in [[Budapest]], grew up in [[Slovakia]], but spent his working life in the [[United States]]. His family emigrated to [[Canada]] in 1938, and subsequently he served in the [[Canadian Forces|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 circuit]]s ([[Bott-Duffin theorem]] from 1949), then switched to pure mathematics.
He studied the [[homotopy theory]] of [[Lie group]]s, using methods from [[Morse theory]], leading to the [[Bott periodicity theorem]] (1956). In the course of this work, he introduced [[Morse theory#Morse-Bott Theory|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 [[Atiyah-Singer index theorem|index theorem]], especially in formulating related [[fixed-point theorem]]s, 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 [http://www.whoi.edu/science/MPC/dept/meetings/atiyah_bott_35.html]). 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 equation]]s, 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.
[[Image:Raoul Bott.jpg|thumb|right|Official photo]]
He is also known in connection with the [[Borel-Bott-Weil theorem]] on representation theory of Lie groups via holomorphic [[sheaf (mathematics)|sheaves]] and their cohomology groups; and for work on [[foliation]]s.
In 1964, he was awarded the [[Oswald Veblen Prize in Geometry]] by the [[American 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 language|Hungarian]]. His Czech stepfather did not, so the principal language at home was [[German language|German]]. He had an English governesses from a young age, so he also spoke perfect [[English language|English]] (and retained a very faint English accent throughout his life). The language of his high school was [[Slovak language|Slovak]]. Despite all this Bott claimed a distaste for learning languages.
==Publications==
*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 {{MR|1321890}}
* 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 {{MR|1321886 }}
*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 0-8176-3646-3{{MR|1290361}}
*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 {{MR|1280032 }}
*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 {{MR|0658304}}
*Bott, Raoul Lectures on K(X). Mathematics Lecture Note Series W. A. Benjamin, Inc., New York-Amsterdam 1969 x+203 pp.{{MR|0258020}}
==External links==
*{{MathGenealogy|id=7583}}
*[http://www.math.harvard.edu/history/bott/index.html Commemorative website at Harvard Math Department]
*[http://www.math.harvard.edu/history/bott/bottbio/index.html "The Life and Works of Raoul Bott"], by Loring Tu
*[http://www.nytimes.com/2006/01/08/national/08bott.html "Raoul Bott, an Innovator in Mathematics, Dies at 82"], ''[[The New York Times]]'', [[January 8]], [[2006]]
{{Wolf Prize in Mathematics}}
{{DEFAULTSORT:Bott, Raoul}}
[[Category:20th century mathematicians]]
[[Category:American mathematicians]]
[[Category:Hungarian mathematicians]]
[[Category:Topologists]]
[[Category:Geometers]]
[[Category:American Jews]]
[[Category:Hungarian Jews]]
[[Category:Harvard University faculty]]
[[Category:University of Michigan faculty]]
[[Category:McGill University alumni]]
[[Category:Carnegie Mellon University alumni]]
[[Category:Foreign Members of the Royal Society]]
[[Category:National Medal of Science laureates]]
[[Category:Wolf Prize in Mathematics laureates]]
[[Category:Cancer deaths]]
[[Category:1923 births]]
[[Category:2005 deaths]]
[[Category:Members of the French Academy of Sciences]]
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[[ja:ラウル・ボット]]
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[[zh:拉乌尔·博特]]