Spinors and the tangent groupoid
Differential Geometry
2019-02-25 v1
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.
Keywords
Cite
@article{arxiv.1902.08351,
title = {Spinors and the tangent groupoid},
author = {Nigel Higson and Zelin Yi},
journal= {arXiv preprint arXiv:1902.08351},
year = {2019}
}