On the analyticity of the bivariant JLO cocycle

Moulay-Tahar Benameur; Alan L. Carey

doi:10.3934/era.2009.16.37

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

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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
2.
Mathematical Sciences Institute, Australian National University, Canberra, ACT. 0200

Received: November 30, 2008

Revised: May 31, 2009

Published: December 2008

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Abstract

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 $C^\infty(B)$.

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Mathematics Subject Classification: 58J30.

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