Differential geometry construction of anomalies and topological invariants in various dimensions

The Lagrangian of non-Abelian tensor gauge fields describes interaction of the Yang-Mills field and massless tensor gauge bosons of increasing helicities. The model allows the existence of metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms. We also found exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential anomalies in various dimensions.