Some Remarks on Gravitational Analogs of Magnetic Charge
  Existing mathematical results are applied to the problem of classifying closed $p$-forms which are locally constructed from Lorentzian metrics on an $n$-dimensional orientable manifold $M$ ($0<p<n$). We show that the only closed, non-exact forms are generated by representatives of cohomology classes of $M$ and $(n-1)$-forms representing $n$-dimensional (with $n$ even) generalizations of the conservation of ``kink number'', which was exhibited by Finkelstein and Misner for $n=4$. The cohomology class that defines the kink number depends only on the diffeomorphism equivalence class of the metric, but a result of Gilkey implies that there is no representative of this cohomology class which is built from the metric, curvature and covariant derivatives of curvature to any finite order. 
C. G. Torre