  By formally separating the post-topological structures such as the  affine, projective, conformal and metric structures from the  manifold, so that these structures are no longer rigidly tied to it,  Riemann deprived them of their formal geometric rigidity and, on the  basis of his infinitesimal geometric standpoint or  “near-geometry”, allowed for the possibility of  interpreting them as mathematical representations of flexible,  dynamical physical structural fields [Strukturfelder] on the manifold of spacetime, geometrical fields that reciprocally interact with  matter.