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On Torsion and Nieh–Yan Form

Using the well-known Chern–Weil formula and its generalization, we systematically construct the Chern–Simons forms and their generalization induced by torsion as well as the Nieh–Yan (N–Y) forms. We also give an argument on the vanishing of integration of N–Y form on any compact manifold without boundary. A systematic construction of N–Y forms in dimensions is also given.