In this talk, I shall present a study of Getzler’s approach to Atiyah-Singer index theorem from the perspective of Alain Connes’ tangent groupoid. Suppose that M is a Riemannian spin manifold and S be its spinor bundle, we shall construct from S a coefficient bundle for the tangent groupoid whose space of smooth compactly supported sections has a convolution algebra structure with an interesting convolution structure. We shall explain how this convolution algebra is related to Getzler’s symbol calculus.

11-25海报.pdf