Hopf algebras and universal Chern classes

摘要

We construct a variant K-n of the Hopf algebra H-n, which acts directly on the noncommutative model for the space of leaves of a general foliation rather than on its frame bundle. We prove that the Hopf cyclic cohomology of K-n is isomorphic to that of the pair. H-n; L-g(n)) and thus consists of the universal Hopf cyclic Chern classes. We also realize these classes in terms of geometric cocycles.