Fibre bundles, connections and cyclic homology

Details Fibre bundles, connections and cyclic homology Fibre bundles, connections and cyclic homology

2005-10-04

arxiv.org/abs/math/0510062v1

Mathematics

Differential Geometry

8 pages ; see also http://www.math.jussieu.fr/~karoubi/

Scientific paper

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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