Quantization and the Tangent Groupoid *
نویسنده
چکیده
This is a survey of the relationship between C *-algebraic deformation quan-tization and the tangent groupoid in noncommutative geometry, emphasizing the role of index theory. We first explain how C *-algebraic versions of deformation quantization are related to the bivariant E-theory of Connes and Higson. With this background, we review how Weyl–Moyal quantization may be described using the tangent groupoid. Subsequently, we explain how the Baum–Connes analytic assembly map in E-theory may be seen as an equivariant version of Weyl–Moyal quantization. Finally, we expose Connes's tangent groupoid proof of the Atiyah– Singer index theorem.
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