Sur le théorème d’Atiyah-Singer. (About the Atiyah-Singer theorem). (French) Zbl 0639.58024
We give a simplified version of Bismut’s probabilistic proof of the index theorem for the Dirac operator. By using Schwartz’s construction of a Brownian motion over a manifold, we expect to give a simpler approach to the computations of stochastic geometry. Our main tool is the calculus of stochastic variations, rather than the splitting of the Wiener space into two pieces. For that reason, we lose the relation with the cohomology of the loop space.
Reviewer: R.Léandre
MSC:
| 58J20 | Index theory and related fixed-point theorems on manifolds |
| 58J65 | Diffusion processes and stochastic analysis on manifolds |
References:
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