ON THE ANALYTICITY OF THE BIVARIANT JLO COCYCLE

The goal of this note is to outline a proof that, for any l >= 0, the JLO bivariant cocycle associated with a family of Dirac type operators along a smooth. bration M -> B over the pair of algebras (C-infinity(M), C-infinity(B)), is entire when we endow C-infinity(M) with the Cl+1 topology and C-infinity(B) with the C-l topology. As a corollary, we deduce that this cocycle is analytic when we consider the Frechet smooth topologies on C-infinity(M) and C-infinity(B).