Hopf algebras, cyclic cohomology and the transverse index theory, by Alain Connes and Henri Moscovici

We present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of a transversally elliptic operator on an arbitrary foliation. The new and crucial ingredient is a certain Hopf algebra associated to the transverse frame bundle. Its cyclic cohomology is defined and shown to be canonically isomorphic to the Gelfand-Fuks cohomology.

Alain Connes <connes@ihes.fr>
Henri Moscovici <henri@math.ohio-state.edu>