Hempel, John2011-07-252011-07-252010Pershell, Karoline. "Some conditions for recognizing a 3-manifold group." (2010) Diss., Rice University. <a href="https://hdl.handle.net/1911/62076">https://hdl.handle.net/1911/62076</a>.https://hdl.handle.net/1911/62076In this work we ask when a group is a 3-manifold group, or more specifically, when does a group presentation come naturally from a Heegaard diagram for a 3-manifold? We will give some conditions for partial answers to this form of the Isomorphism Problem by addressing how the presentation associated to a diagram for a splitting is related to the fundamental group of a 3-manifold, still using diagrams as a tool to answer these questions. In the process, we determine an invariant of groups (by way of group presentations) for how far such presentations are from 3-manifolds.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.MathematicsThesisTHESIS MATH. 2010 PERSHELL