Totally geodesic surfaces in hyperbolic 3-manifolds
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This thesis investigates the topology and geometry of hyperbolic 3-manifolds containing totally geodesic surfaces. In chapter 2 we find algebraic invariants associated to several families of hyperbolic 3-manifolds with totally geodesic boundary. In chapter 3 we describe examples of hyperbolic knot complements in rational homology 3-spheres containing closed embedded totally geodesic surfaces.