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Article Dans Une Revue J. K-theory Année : 2013

Higher spectral flow and an entire bivariant JLO cocycle

Résumé

Given a smooth fibration of closed manifolds and a family of generalised Dirac operators along the fibers, we define an associated bivariant JLO cocycle. We then prove that, for any $\ell \geq 0$, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the $C^{\ell+1}$ topology and functions on the base manifold with the $C^\ell$ topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

Dates et versions

hal-00789817 , version 1 (18-02-2013)

Identifiants

Citer

Moulay-Tahar Benameur, Alan L. Carey. Higher spectral flow and an entire bivariant JLO cocycle. J. K-theory, 2013, 11, pp.183-232. ⟨10.1017/is012008031jkt193⟩. ⟨hal-00789817⟩
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