nLab Raoul Bott

Selected writings

Raoul Bott (1923–2005) was one of the great 20th century topologists and geometers. Among his famous works, one should mention the Bott periodicity theorem (of importance in K-theory), studies in Morse theory (including the study of Bott–Morse functions), the Borel–Weil–Bott theorem in geometric representation theory, the study of fixed point (localization) formulas (the Atiyah–Bott fixed point theorem) and the Atiyah-Bott-Patodi slick proof of the index theorem via the heat kernel expansion.

Selected writings

Introducing the concept and terminology of the Pontrjagin product on the ordinary homology of based loop spaces:

and application to the case of Lie groups:

Introducing Bott periodicity:

  • Raoul Bott, The Stable Homotopy of the Classical Groups, Proceedings of the National Academy of Sciences of the United States of America 43 10 (1957) 933-935 [jstor:89403]

Introducing the Atiyah-Bott-Shapiro orientation MSpin\toKO and MSpinc\toKU:

On topological K-theory:

On the Chern-Weil homomorphism:

On differential forms in algebraic topology:

On the simplicial de Rham complex and equivariant de Rham cohomology:

On the rigidity theorem for elliptic genera:

  • Raoul Bott, Clifford Taubes, On the Rigidity Theorems of Witten, Journal of the American Mathematical Society Vol. 2, No. 1 (Jan., 1989), pp. 137-186 (doi:10.2307/1990915)

  • Raoul Bott, On the Fixed Point Formula and the Rigidity Theorems of Witten, Lectures at Cargése 1987. In: ’t Hooft G., Jaffe A., Mack G., Mitter P.K., Stora R. (eds) Nonperturbative Quantum Field Theory. NATO ASI Series (Series B: Physics), vol 185. Springer (1988) (doi:10.1007/978-1-4613-0729-7_2)

category: people

Last revised on November 23, 2023 at 12:25:26. See the history of this page for a list of all contributions to it.