Secondary Characteristic Classes and Cyclic Cohomology of Hopf Algebras

TL;DR

This paper constructs cyclic cocycles for equivariant characteristic classes of bundles, generalizing Connes' Godbillon-Vey cocycle, using the cyclic cohomology of Hopf algebras.

Contribution

It introduces a new construction of cyclic cocycles for equivariant bundles, extending existing theories with a Hopf algebra approach.

Findings

Generalizes Connes' Godbillon-Vey cyclic cocycle

Uses Connes-Moscovici's cyclic cohomology of Hopf algebras

Provides explicit formulas for equivariant characteristic classes

Abstract

We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.