Equivariant Chern classes in Hopf cyclic cohomology

TL;DR

This paper introduces a geometric method inspired by Chern-Weil theory to explicitly construct cocycles representing Hopf cyclic cohomology classes of H(n), enriching the understanding of universal Hopf cyclic Chern classes.

Contribution

It provides a new geometric approach to explicitly describe universal Hopf cyclic Chern classes relative to GL(n, R).

Findings

Explicit cocycle constructions for Hopf cyclic cohomology classes

Complementary to previous geometric realizations of foliation classes

Enhanced understanding of universal Hopf cyclic Chern classes

Abstract

We present a geometric approach, in the spirit of the Chern-Weil theory, for constructing cocycles representing the classes of the Hopf cyclic cohomology of the Hopf algebra H(n) relative to GL(n, R). This provides an explicit description of the universal Hopf cyclic Chern classes, which complements our earlier geometric realization of the Hopf cyclic characteristic classes of foliations.