We define secondary theories and characteristic classes for simplicial smooth
manifolds generalizing Karoubi’s multiplicative K–theory and multiplicative
cohomology groups for smooth manifolds.
As a special case we get versions of the groups of differential characters of
Cheeger and Simons for simplicial smooth manifolds.
Special examples include classifying spaces of Lie groups and Lie groupoids.
Keywords
multiplicative K–theory,
multiplicative cohomology, differential characters, smooth
simplicial manifolds, simplicial de Rham theory