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In this article we shall consider the tensor gauge fields which are possibleto embed into the existing framework of generalized YM theory and thereforeallows to construct the gauge invariant and metric independent forms in 2n+4and 2n+2 dimensions. These new forms are analogous to thePontryagin-Chern-Simons densities in YM gauge theory and to the correspondingseries of densities in 2n+3 dimensions constructed recently in arXiv:1205.0027.

Non-Abelian tensor gauge fields and new topological invariants