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.
Loring Tu about Raoul Bott in history web at Harvard: http://www.math.harvard.edu/history/bott/bottbio/bottbio.html
Raoul Bott, Loring Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer 1982. xiv+331 pp. (doi:10.1007/978-1-4757-3951-0, pdf)
(on differential forms in algebraic topology)
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