Reid, Alan W2022-09-262022-09-262022-052022-04-22May 2022Stagner, William. "Filling links and minimal surfaces in 3-manifolds." (2022) Diss., Rice University. <a href="https://hdl.handle.net/1911/113390">https://hdl.handle.net/1911/113390</a>.https://hdl.handle.net/1911/113390This thesis studies this existence of filling links 3-manifolds. A link L in a 3-manifold M is filling in M if, for any spine G of M disjoint from L, π_1(G) injects into π_1(M-L). Conceptually, a filling link cuts through all of the topology 3-manifold. These links were first studied by Freedman-Krushkal in the concrete case of the 3-torus M = T^3, but they leave open the question of whether a filling link actually exists in T^3. We answer this question affirmatively by proving in fact that every closed, orientable 3-manifold M with fundamental group of rank 3 contains a filling link.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.3-manifoldshyperbolic manifoldsminimal surfaceslow-dimensional topologyThesis2022-09-26