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Article Dans Une Revue Journal of Noncommutative Geometry Année : 2020

The index of G-transversally elliptic families in KK-theory

Résumé

We define and study the index map for families of G-transversally elliptic operators and introduce the multiplicity for a given irreducible representation as a virtual bundle over the base of the fibration. We then prove the usual axiomatic properties for the index map extending the Atiyah-Singer results [1]. Finally, we compute the cup product of our index class against the K-homology class of an elliptic operator on the base. Our approach is based on the functorial properties of Kasparov's cup product, and relies on some constructions due to Connes-Skandalis and to Hilsum-Skandalis.
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Dates et versions

hal-01873318 , version 1 (13-09-2018)

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Alexandre Baldare. The index of G-transversally elliptic families in KK-theory. Journal of Noncommutative Geometry, 2020, 14 (3), pp.1129-1169. ⟨10.4171/JNCG/389⟩. ⟨hal-01873318⟩
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