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.
Original language | English (US) |
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Pages (from-to) | 1677-1720 |
Number of pages | 44 |
Journal | Documenta Mathematica |
Volume | 24 |
DOIs | |
State | Published - 2019 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)