Dehn paternity bounds and hyperbolicity tests

Thesis advisor: George R. MeyerhoffRecent advances in normal surface algorithms enable the determination by computer of the hyperbolicity of compact orientable 3-manifolds with zero Euler characteristic and nonempty boundary. Recent advances in hyperbolic geometry enable the determination by computer of the Dehn paternity relation between two orientable compact hyperbolic 3-manifolds. Presented here is an exposition of these developments, along with prototype implementations of one of these determinations in software. These have applications to two questions about Mom technology.Thesis (PhD) — Boston College, 2015.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Mathematics