What remains is to work through the discrete symmetries of the above construction. There are several that appear to generalize P-symmetry and T-symmetry. Identifying the p dimensions with time, and the q dimensions with space, one can reverse the tangent vectors in the p dimensional subspace to get time reversal, and flipping the direction of the q dimensions corresponds to parity. The C-symmetry can be identified with the reflection on the line bundle. To tie all of these together into a knot, one finally has the concept of transposition, in that elements of the Clifford algebra can be written in reversed (transposed) order. The net result is that not only do the conventional physics ideas of fields pass over to the general Riemannian setting, but also the ideas of the discrete symmetries.