Secondary Theories for etale groupoids

TL;DR

This paper extends secondary theories and characteristic classes to smooth etale groupoids, generalizing existing concepts for manifolds and orbifolds, and introduces new structures in differential cohomology.

Contribution

It develops secondary theories and characteristic classes specifically for smooth etale groupoids, broadening the scope of multiplicative K-theory and cohomology.

Findings

Defines secondary theories for smooth etale groupoids

Provides versions of differential characters for orbifolds

Generalizes multiplicative K-theory to groupoids

Abstract

Generalizing Karoubi's multiplicative K-theory and multiplicative cohomology groups for smooth manifolds we define secondary theories and characteristic classes for smooth etale groupoids. As special cases we obtain versions of the groups of differential characters for smooth etale groupoids and for orbifolds.