Spinors and the Tangent Groupoid

  • Nigel Higson

    Department of Mathematics, Penn State University, University Park, PA 16802, USA
  • Zelin Yi

    Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
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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. 1677–1720

DOI 10.4171/DM/712