Reid, Alan W.1663531732008-08-282008-08-282007http://hdl.handle.net/2152/3025textThis 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.electronicengCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.Curves on surfacesGeometry, HyperbolicThree-manifolds (Topology)Thesis