English

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/