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


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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