## Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem.(English)Zbl 0543.58026

Some results on Clifford algebras and the spinor representation, as well as an extension of a symbol calculus on spin manifolds to pseudodifferential operators are combined to simplify the proof of the Atiyah-Singer index theorem for the Dirac operator on a spin manifold.
Reviewer: N. Papaghiuc

### MSC:

 58J40 Pseudodifferential and Fourier integral operators on manifolds 35S05 Pseudodifferential operators as generalizations of partial differential operators 58J20 Index theory and related fixed-point theorems on manifolds 53C27 Spin and Spin$${}^c$$ geometry 53C20 Global Riemannian geometry, including pinching 58A50 Supermanifolds and graded manifolds
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### References:

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