Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: John Luecke. Vita. Includes bibliographical references. Available also from UMI company.

Thesis (Ph. D.)--University of Oregon, 2004. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 123-125). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph. D.)--University of Florida. 1981. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 68-71).

Thesis (Ph.D.)--Aberdeen University, 2008. / Title from web page (viewed on Mar. 2, 2009). Includes bibliographical references.

This paper focuses on generalizing unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces. The paper introduces a related algebraic structure known as twisted virtual bikeigebras whose axioms are motivated by the twisted virtual handlebody-link Reidemeister moves. In the research, twisted virtual bikeigebras are used to dene X-colorability for twisted virtual handlebody-links and define an integer-valued invariant of twisted virtual handlebody-links. The paper also includes example computations of the new invariants and use them to distinguish some twisted virtual handlebody-links.

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The uniform thickness of knots has been used to investigate knotted polymers and DNA strands. Even though these structures carry great length, it is unusual for them to contain knots. However, when they do, it can cause gene malfunctions. In fact, scientist have demonstrated that knotting may cause a loss of genetic material by blocking DNA replication and also blocking transcription of a gene into its active protein. Since it is possible for biological structures, such as polymers and DNA strands, to exhibit forces or charges of different strengths the idea of a non uniform thickness of a knot is explored. In his work, O. Durumeric provides a definition for the non uniform thickness. This thesis will provide an alternative characterization for the non uniform thickness of a knot, which is more conducive to computer calculations.

Baseilhac and Benedetti have created a quantum hyperbolic knot invariant similar to the colored Jones polynomial. Their invariant is based on the polyhedral decomposition of the knot complement into ideal tetrahedra. The edges of the tetrahedra are assigned cross ratios based on their interior angles. Additionally, these edges are decorated with charges and flattenings which can be determined by assigning weights to the longitude and meridian of the boundary torus of a neighborhood of the knot. Baseilhac and Benedetti then use a summation of matrix dilogarithms to get their invariants. This thesis investigates these invariants for the figure eight knot. In fact, it will be shown that the volume of the complete hyperbolic structure of the knot serves as an upper bound for the growth of the invariants.