Homology of Curves and Surfaces in Closed Hyperbolic 3-manifolds
نویسندگان
چکیده
Among other things, we prove the following two topologcal statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manifold has a positve integral multiple represented by an oriented connected closed π1-injectively immersed quasiFuchsian subsurface. Second, every rationally null-homologous, π1-injectively immersed oriented closed 1-submanifold in a closed hyperbolic 3-manifold has an equidegree finite cover which bounds an oriented connected compact π1injective immersed quasi-Fuchsian subsurface. In part, we exploit techniques developed by Kahn and Markovic in [KM1, KM2], but we only distill geometric and topological ingredients from those papers so no hard analysis is involved in this paper.
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