# American Institute of Mathematical Sciences

2009, 16: 37-43. doi: 10.3934/era.2009.16.37

## On the analyticity of the bivariant JLO cocycle

 1 UMR 7122, Universit Paul Verlaine-Metz, Bt. A, Ile du Saulcy, F-57045 METZ Cedex 1, France 2 Mathematical Sciences Institute, Australian National University, Canberra, ACT. 0200, Australia

Received  December 2008 Revised  June 2009 Published  July 2009

The goal of this note is to outline a proof that, for any l $\geq 0$, the JLO bivariant cocycle associated with a family of Dirac type operators along a smooth fibration $M\to B$ over the pair of algebras $(C^\infty (M), C^\infty(B))$, is entire when we endow $C^\infty(M)$ with the $C^{l+1}$ topology and $C^\infty(B)$ with the $C^{l}$ topology. As a corollary, we deduce that this cocycle is analytic when we consider the Fréchet smooth topologies on $C^\infty(M)$ and $C^\infty(B)$.
Citation: Moulay-Tahar Benameur, Alan L. Carey. On the analyticity of the bivariant JLO cocycle. Electronic Research Announcements, 2009, 16: 37-43. doi: 10.3934/era.2009.16.37
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