Comments on: "Operator $K$-theory for the group SU(n,1)" by P. Julg and G. Kasparov

Abstract

In this note we point out and fill a gap in the proof by Julg-Kasparov of the Baum-Connes conjecture with coefficients for discrete subgroups of $\op{SU}(n,1)$. The issue at stake is the proof that the complex powers of the contact Laplacian are element of the Heisenberg calculus. In particular, we explain why we cannot implement into the setting of the Heisenberg calculus the classical Seeley's approach to complex powers.