Hyperbolic spaces H~n [7] are models of an infinite cosmos with constant negative curvature. Moreover they provide universal covering spaces for compact finite manifolds M of nontrivial topology with the same metric and curvature. The double torus T∪T and the Weber-Seifert manifold are hyperbolic manifolds M covered by H~2, H~3 respectively. Both display closed geodesies with observable effects on the distribution of matter. The preimage and image points under any homotopy g ∈ π(M) when acting on H~n are identified on M. Therefore any closed geodesic corresponds to a homotopy g. It is shown that Ihe closed geodesies on M associated with g can be compared and classified in length and relative direction by orbits under the continuous normalizers N_g, g ∈π (M).
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