Abstract: Joint work with Tobias Diez, Karl-Hermann Neeb, and Bas Janssens.
Differential characters of degree one are in bijection with isomorphism classes of
principal circle bundles with connection, via the holonomy map. We define differential
characters of higher degree (higher dimensional holonomy) and we describe some of
their properties following [BB]. For a compact manifold $S$, we show how differential
characters on $C^\infty(S,M)$, as well as on the nonlinear Grassmannian $Gr^S(M)$
of submanifolds of $M$ of type $S$, are obtained by combining in a natural way
differential characters on S and on M. The aim is to obtain degree one differential
characters on these Fr\'echet manifolds, in order to use the prequantization central
extension for integrating Lichnerowicz 2-cocycles on the Lie algebra of divergence
free vector fields.