The life and works of Raoul Bott

Loring W. Tu

Date: January 4, 2002

Department of Mathematics
Tufts University
Medford, MA 02155-7049

[email protected]

In a career spanning five decades, Raoul Bott has wrought profound changes on the landscape of geometry and topology. It is a daunting task to improve upon his own reminiscences [B3], [B4], [B1] and commentaries on papers [B5], punctuated as they are by insight, colorful turns of phrases and amusing anecdotes. This article, based on his writings and on interviews and correspondences with people who have known him, aims to serve as an introduction to his life and works so far.

• Early years
• Canada
• Sermon
• Mathematical Career
• Dunster House
• Bott as a teacher
• Honors and Awards
• Impedance
• Morse theory
• Lie groups and homogeneous spaces
• Index of a closed geodesic
• Homogeneous vector bundles
• The periodicity theorem
• Clifford algebras
• The index theorem for homogeneous differential operators
• Nevanlinna theory and the Bott-Chern classes
• Characteristic numbers and the Bott residue
• The Atiyah-Bott fixed point theorem
• Obstruction to integrability
• The cohomology of the vector fields on a manifold
• Localization in equivariant cohomology
• Yang-Mills equations over Riemann surfaces
• Witten's rigidity theorem
• Bibliography