Geodesic
Spinors and the Tangent Groupoid
Documenta mathematica, Tome 24 (2019), pp. 1677-1720
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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.
DOI : 10.4171/dm/712
Classification : 58B34, 58J20
Mots-clés : tangent groupoid, spinor bundle, local index theorem 
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     author = {Zelin Yi and Nigel Higson},
     title = {Spinors and the {Tangent} {Groupoid}},
     journal = {Documenta mathematica},
     pages = {1677--1720},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/712},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/712/}
}
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Zelin Yi; Nigel Higson. Spinors and the Tangent Groupoid. Documenta mathematica, Tome 24 (2019), pp. 1677-1720. doi: 10.4171/dm/712

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