Document Type

Dissertation

Date of Degree

Fall 2009

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Charles Frohman

Abstract

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.

Keywords

Baseilhac, Benedetti, hyperbolic, invariant, knot, topology

Pages

v, 69 pages

Bibliography

Includes bibliographical references (page 60).

Copyright

Copyright 2009 Heather Michelle Mollé

Included in

Mathematics Commons

Share

COinS