Geodesic
Spinors and the Tangent Groupoid
Documenta mathematica, Tome 24 (2019), pp. 1677-1720.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The purpose of this article is to study Ezra Getzler's approach to the Atiyah-Singer index theorem from the perspective of Alain Connes' tangent groupoid. We shall construct a ``rescaled'' spinor bundle on the tangent groupoid, define a convolution operation on its smooth, compactly supported sections, and explain how the algebra so-obtained incorporates Getzler's symbol calculus.
Classification : 58B34, 58J20
Keywords: tangent groupoid, spinor bundle, local index theorem 
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     title = {Spinors and the {Tangent} {Groupoid}},
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Higson, Nigel; Yi, Zelin. Spinors and the Tangent Groupoid. Documenta mathematica, Tome 24 (2019), pp. 1677-1720. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a23/