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The Life and Works of Raoul Bott

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Raoul Bott: Collected Papers

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Abstract

Raoul Bott passed away on December 20, 2005. In a career spanning five decades, he 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 is an updated reprint of one that first appeared in the book The Founders of Index Theory: Reminiscences of Atiyah, Bott, Hirzebruch, and Singer (edited by S.-T. Yau, International Press, 2003). Taking a personal interest in the project, Raoul Bott introduced me to some of his friends and gave me access to his files. After the original article was completed in June 2000, he read it and verified the essential correctness of the accounts of both his life and his works. In the interest of preserving its official imprimatur as an authorized biography, the only changes I made to the 2003 version consist of this introductory paragraph, an update of the awards he received, and the suppression of a bibliography of his works not referenced in the article.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, USA

    Loring W. Tu

Authors
  1. Loring W. Tu
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, USA

    Loring W. Tu

Papers of Raoul Bott Discussed in this Article

Papers of Raoul Bott Discussed in this Article

  1. [1]

    with R. J. Duffin) Impedance synthesis without use nof transformers,J. Appl. Phys. 20(1949), 816.

  2. [8]

    On torsion in Lie groups, Proc. NAS 40(1954), 586-588.

  3. [9]

    Nondegenerate critical manifolds, Ann. of Math. 60(1954), 248-261.

  4. [12]

    (with H. Samelson) The cohomology ring of G/T, Proc. NAS 41(1955), 490–493.

  5. [14]

    (On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. IX(1956), 171–206.

  6. [15]

    Homogeneous vector bundles, Ann. of Math. 66(1957), 933-935.

  7. [24]

    The stable homotopy of the classical groups, Ann. of Math. 70(1959), 313-337.

  8. [33]

    (with M. F. Atiyah and A. Shapiro) Clifford modules, Topology 3(1965), 3-38.

  9. [37]

    The index theorem for homogeneous differential operators, in: Differential and Combinatorial Topology: A Symposium in Honor of Marston Morse, Princeton, (1964), 167-186.

  10. [38]

    (with S. Chern) Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections, Acta Mathematica 114(1964), 71-112.

  11. [41]

    Vector fields and characteristic numbers, Mich. Math. J. 14(1967), 231-244.

  12. [42]

    (with M. F. Atiyah) A Lefschetz fixed point formula for elliptic complexes: I, Ann. of Math. 86(1967), 374-407.

  13. [43]

    A residue formula for holomorphic vector fields, J. Differential Geom. 1(1967), 311-330.

  14. [44]

    (with M. F. Atiyah) A Lefschetz fixed point formula for elliptic complexes: II, Ann. of Math. 88(1968), 451-491.

  15. [51]

    On a topological obstruction to integrability, in: Global Analysis, Proceedings of Symposia in Pure Math. XVI(1970), 127-131.

  16. [71]

    (with G. Segal) The cohomology of the vector fields on a manifold, Topology 16(1977), 285-298.

  17. [81]

    (with M. F. Atiyah) The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308(1982), 524-615.

  18. [82]

    (with M. F. Atiyah) The moment map and equivariant cohomology, Topology 23(1984), 1-28.

  19. [91]

    (with C. Taubes) On the rigidity theorem of Witten, J. of the Amer. Math. Soc. 2(1989), 137-186.

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Tu, L.W. (2017). The Life and Works of Raoul Bott. In: Tu, L. (eds) Raoul Bott: Collected Papers . Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51781-0_4

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