American Institute of Mathematical Sciences

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

On the analyticity of the bivariant JLO cocycle

Moulay-Tahar Benameur 1, and  Alan L. Carey 2,

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 $C^\infty(B)$.
Keywords: JLO, Noncommutative geometry, Families Index..
Mathematics Subject Classification: 58J3.
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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