Hopf algebra ${\mathcal{K}}_n$ and universal Chern classes

Abstract

We construct a variant ${\mathcal{K}}_n$ of the Hopf algebra ${\mathcal{H}}_n$, which acts directly on the noncommutative model for the generic space of leaves rather than on its frame bundle. We prove that the Hopf cyclic cohomology of ${\mathcal{K}}_n$ is isomorphic to that of the pair $({\mathcal{H}}_n,{\mathrm{GL}}_n)$ and thus consists of the universal Hopf cyclic classes. We then realize these classes in terms of geometric cocycles.

44 pages, minore changes, published in Journal of Noncommutative Geometry

References in corpus (2)

• Hopf algebras, cyclic cohomology and the transverse index theory
• Equivariant Chern classes in Hopf cyclic cohomology