Spinors and the tangent groupoid

Nigel Higson; Zelin Yi

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arXiv · 1902.08351

Spinors and the tangent groupoid

Nigel Higson·Zelin Yi

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Abstract

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.

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BibTeX RIS

Nigel Higson, Zelin Yi. 2019-02-22. Spinors and the tangent groupoid. https://arxiv.org/abs/1902.08351

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