Fibre bundles, connections and cyclic homology
Differential Geometry
2007-05-23 v1 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.math/0510062,
title = {Fibre bundles, connections and cyclic homology},
author = {Max Karoubi},
journal= {arXiv preprint arXiv:math/0510062},
year = {2007}
}
Comments
8 pages ; see also http://www.math.jussieu.fr/~karoubi/