Abstract.
Any closed current on the base of a compact fibration gives rise to a cyclic cocycle on the smooth convolution algebra. We prove that such cocycle furnishes additive maps from the vertically equivariant K-theory to the scalars. This enables to associate to any closed current on the base of the fibration, a Lefschetz formula for fiber-preserving isometries. Using geometric operators on the base, we deduce the integrality of some characteristic numbers.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 28 June 2001 / Published online: 1 February 2002
Rights and permissions
About this article
Cite this article
Benameur, MT. Cyclic cohomology and the family Lefschetz theorem. Math Ann 323, 97–121 (2002). https://doi.org/10.1007/s002080100298
Issue Date:
DOI: https://doi.org/10.1007/s002080100298