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Complex powers of the contact Laplacian and the Baum-Connes conjecture for SU(n,1)

Raphael Ponge
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Abstract

This paper is an extended version of math.OA/0601528 where we point out and remedy a gap in the proof by P. Julg and G. Kasparov of the Baum-Connes conjecture for discrete subgroups of SU(n,1). In particular, here we explain in details why the non-microlocality of the Heisenberg calculus prevents us from implementing into this framework the classical approach of Seeley to pseudodifferential complex powers, which was the main issue at stake in math.OA/0601528.

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Raphael Ponge. 2006-04-25. Complex powers of the contact Laplacian and the Baum-Connes conjecture for SU(n,1). https://arxiv.org/abs/math/0601529

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