Reid, Alan W2024-05-222024-05-222024-052024-04-17May 2024Edelman-Munoz, Sara. Thin Surface Subgroups in Non-uniform Arithmetic Lattices in SO+(n,1). (2024). https://hdl.handle.net/1911/116158https://hdl.handle.net/1911/116158In this thesis I show that the fundamental groups of all non-compact, arithmetic, hyperbolic, n-manifolds for n $\geq$ 4 have thin surface subgroups. As a consequence of the proof of this theorem I show that the fundamental groups of the doubles of cusped, arithmetic, hyperbolic manifolds are GFERF.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Arithmetic groupsthin groupshyperbolic geometryThesis2024-05-22