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Banach KK-theory and the Baum-Connes conjecture

Vincent Lafforgue
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Abstract

The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group $C^*$-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series representations of connected semi-simple Lie groups.

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Vincent Lafforgue. 2003-04-22. Banach KK-theory and the Baum-Connes conjecture. https://arxiv.org/abs/math/0304342

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