Higher Chern-Simons based on (2-)crossed modules

We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized connections which consist of higher connections. Then we establish the generalized Chern-Simons forms to get the higher Chern-Simons actions. Finally, we develop the higher second Chern forms and Chern-Weil theorems.

Automated summary

This paper presents higher Chern-Simons theories based on (2-)crossed modules. It starts by generalizing the differential forms in Generalized Differential Calculus and defining the corresponding generalized connections, which consist of higher connections. Then, it establishes the generalized Chern-Simons forms to obtain the higher Chern-Simons actions. Finally, it develops the higher second Chern forms and Chern-Weil theorems.