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Immersing almost geodesic surfaces in a closed hyperbolic three manifold

Immersing almost geodesic surfaces in a closed hyperbolic three manifold

Let M 3 be a closed hyperbolic three manifold.We construct closed surfaces that map by immersions into M 3 so that for each, one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.