JournalsjncgVol. 11, No. 1pp. 71–109

Hopf algebras and universal Chern classes

  • Henri Moscovici

    The Ohio State University, Columbus, USA
  • Bahram Rangipour

    University of New Brunswick, Fredericton, Canada
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Abstract

We construct a variant Kn\mathcal K_n of the Hopf algebra Hn\mathcal 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 Kn\mathcal K_n is isomorphic to that of the pair (Hn,gln)(\mathcal H_n, \mathfrak {gl}_n) and thus consists of the universal Hopf cyclic Chern classes. We also realize these classes in terms of geometric cocycles.

Cite this article

Henri Moscovici, Bahram Rangipour, Hopf algebras and universal Chern classes. J. Noncommut. Geom. 11 (2017), no. 1, pp. 71–109

DOI 10.4171/JNCG/11-1-3