Higson, Nigel; Yi, Zelin

Spinors and the Tangent Groupoid

Doc. Math. 24, 1677-1720 (2019)
DOI: 10.25537/dm.2019v24.1677-1720
Communicated by Eckhard Meinrenken

Summary

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.

Mathematics Subject Classification

58B34, 58J20

Keywords/Phrases

tangent groupoid, spinor bundle, local index theorem

References

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Affiliation

Higson, Nigel
Department of Mathematics, Penn State University, University Park, PA 16802, USA
Yi, Zelin
Chern Institute of Mathematics, Nankai University, Tianjin 300071, Chin

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