Une approche probabiliste du théorème de l'indice (Atiyah-Singer)

Robert Azencott

Séminaire Bourbaki (1984-1985)

  • Volume: 27, page 7-18
  • ISSN: 0303-1179

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Azencott, Robert. "Une approche probabiliste du théorème de l'indice (Atiyah-Singer)." Séminaire Bourbaki 27 (1984-1985): 7-18. <http://eudml.org/doc/110054>.

@article{Azencott1984-1985,
author = {Azencott, Robert},
journal = {Séminaire Bourbaki},
keywords = {Clifford and Heisenberg algebras; spinor bundle; heat equation; stochastic differential equations; index formula},
language = {fre},
pages = {7-18},
publisher = {Société Mathématique de France},
title = {Une approche probabiliste du théorème de l'indice (Atiyah-Singer)},
url = {http://eudml.org/doc/110054},
volume = {27},
year = {1984-1985},
}

TY - JOUR
AU - Azencott, Robert
TI - Une approche probabiliste du théorème de l'indice (Atiyah-Singer)
JO - Séminaire Bourbaki
PY - 1984-1985
PB - Société Mathématique de France
VL - 27
SP - 7
EP - 18
LA - fre
KW - Clifford and Heisenberg algebras; spinor bundle; heat equation; stochastic differential equations; index formula
UR - http://eudml.org/doc/110054
ER -

References

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  1. [1] M. Atiyah, R. Bott, V. Patodi - Heat equation and index theorem, Invent. Math.19(1973), 279-330. Zbl0257.58008MR650828
  2. [2] M. Atiyah, I. Singer - Index of elliptic operators I, II, Ann. Math.87(1968), 484-530, 546-604. Zbl0164.24001MR236950
  3. [3] R. Azencott - Densité des diffusions en temps petit, Sém. Proba. XVIII, Lect. Notes in Math.1059(1984), 402-498. Zbl0546.60079MR770974
  4. [4] N. Berline, M. Vergne - Calcul de l'indice équivariant de l'opérateur de Dirac par la méthode de la chaleur, à paraître. Zbl0566.58033
  5. [5] J.-M. Bismut - Mécanique Aléatoire, Lect. Notes in Math., Springer-Verlag1981. Zbl0457.60002MR629977
  6. [6] J.-M. Bismut - Large deviations and Malliavin calculus, Birkhäuser1984. Zbl0537.35003MR755001
  7. [7] J.-M. Bismut - The Atiyah-Singer theorems : a probabilistic approach I, II, J. Funct. Anal.57(1984), 56-98, 329-348. Zbl0538.58033MR756173
  8. [8] E. Getzler - Pseudo-differential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys.92(1983), 163-178. Zbl0543.58026MR728863
  9. [9] P. Gilkey - Curvature and eigenvalues of the Laplacian, Adv. in Math.10(1973), 344-382 Zbl0259.58010MR324731
  10. [10] N. Hitchin - Harmonic Spinors, Adv. in Math.14(1974), 1-55. Zbl0284.58016MR358873
  11. [11] Kanaï - Short time asymptotics for fundamental solutions of partial differential equations, Comn. Part. Diff. Equ.2(1977), 781-830. Zbl0381.35039
  12. [12] P. Malliavin - Stochastic calculus of variations and hypoelliptic operators, Proc. Int. Conf. Stoch. Diff. Equ. Kyoto1976, 195-263, N.Y.Wiley1978. Zbl0411.60060MR536013
  13. [13] S. Molchanov - Diffusions and Riemannian geometry, Russ. Math. Surveys30 (1975), 1-63. Zbl0315.53026

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