Spinors and the Tangent Groupoid
Nigel HigsonDepartment of Mathematics, Penn State University, University Park, PA 16802, USA
Zelin YiChern Institute of Mathematics, Nankai University, Tianjin 300071, China
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.
Cite this article
Nigel Higson, Zelin Yi, Spinors and the Tangent Groupoid. Doc. Math. 24 (2019), pp. 1677–1720DOI 10.4171/DM/712