On the analyticity of the bivariant JLO cocycle

Benameur, Moulay-Tahar; Carey, Alan

Cultural advice

The Australian National University acknowledges, celebrates and pays our respects to the Ngunnawal and Ngambri people of the Canberra region and to all First Nations Australians on whose traditional lands we meet and work, and whose cultures are among the oldest continuing cultures in human history.

Aboriginal and Torres Strait Islander peoples are advised that ANU Library collections may include images, names, voices, and other representations of deceased persons.

Material in the collection may contain terms, language or views that reflect the period in which the item was created and may be considered inappropriate today.

On the analyticity of the bivariant JLO cocycle

Date

2009

Authors

Benameur, Moulay-Tahar

Carey, Alan

Publisher

American Mathematical Society

Abstract

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 fibration M → B over the pair of algebras (C∞(M), C∞(B)), is entire when we endow C∞(M) with the Cℓ+1 topology and C∞(B) with the Cℓ topology. As a corollary, we deduce that this cocycle is analytic when we consider the Fréchet smooth topologies on C∞(M) and C∞(B).