The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.
Inventiones mathematicae, Tome 83 (1986), pp. 91-152.

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Mots-clés : heat equation formula for the index, connections on infinite-dimensional bundles, Atiyah-Singer index theorem, superconnections, stochastic differential calculus
@article{IM_1986__83_143306,
     author = {Jean-Michel Bismut},
     title = {The {Atiyah-Singer} index theorem for families of {Dirac} operators: {Two} heat equation proofs.},
     journal = {Inventiones mathematicae},
     pages = {91--152},
     publisher = {mathdoc},
     volume = {83},
     year = {1986},
     zbl = {0592.58047},
     url = {http://geodesic.mathdoc.fr/item/IM_1986__83_143306/}
}
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Jean-Michel Bismut. The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.. Inventiones mathematicae, Tome 83 (1986), pp. 91-152. http://geodesic.mathdoc.fr/item/IM_1986__83_143306/