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Fibre bundles, connections and cyclic homology

Max Karoubi
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Abstract

This is a survey paper, starting from the general notion of coordinate bundle taken from Steenrod. Its aim is to provide a motivation for the introduction of cyclic homology (and the closely related noncommutative de Rham cohomology) by Connes, Tsygan and the author. The bridge is made through a generalization of Chern-Weil theory, explained in a very concrete manner through the transition functions of the bundles involved. The final result is a "Chern character" introduced by Connes and the author in the framework of K-theory and functional analysis.

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Max Karoubi. 2005-10-04. Fibre bundles, connections and cyclic homology. https://arxiv.org/abs/math/0510062

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