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  • All fields: 3-manifolds
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    • A Toolkit for the Construction and Understanding of 3-Manifolds

    • A Toolkit for the Construction and Understanding of 3-Manifolds

    • Twist construction, bitwist construction, 3-manifolds, Dehn surgery, Heegaard splitting, Heegaard diagram.

    • Since our world is experienced locally in three-dimensional space, students of mathematics struggle to visualize and understand objects which do not fit into three-dimensional space. 3-manifolds are locally three-dimensional, but do not fit into...
    • ETD
    • Subdivision Rules, 3-Manifolds, and Circle Packings

    • Subdivision Rules, 3-Manifolds, and Circle Packings

    • LaTeX, PDF, BYU, Math, Thesis, subdivision, rules, manifold, 3-manifold, circle, packings, infinity, space, geometries, Perelman, torus, hyperbolic, unbounded, valence

    • We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all...
    • ETD
    • Wild Low-Dimensional Topology and Dynamics

    • Wild Low-Dimensional Topology and Dynamics

    • Sharkovskii's Theorem, periodic points, solenoids, 3-manifolds, fundamental group, Peano continua, homotopy invariants

    • In this dissertation we discuss various results for spaces that are wild, i.e. not locally simply connected. We first discuss periodic properties of maps from a given space to itself, similar to Sharkovskii's Theorem for interval maps. We study...
    • ETD
    • Unknotting Tunnels of Hyperbolic Tunnel Number n Manifolds

    • Unknotting Tunnels of Hyperbolic Tunnel Number n Manifolds

    • Hyperbolic Geometry, Hyperbolic 3-manifolds, Unknotting Tunnel, Ford Domain, Knot Theory

    • Adams conjectured that unknotting tunnels of tunnel number 1 manifolds are always isotopic to a geodesic. We generalize this question to tunnel number n manifolds. We find that there exist complete hyperbolic structures and a choice of spine of a...
    • ETD

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