Date of Degree
2009
Document Type
dissertation
Degree Name
PhD (Doctor of Philosophy)
Department
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.
Pages
v, 69
Bibliography
60
Copyright
Copyright 2009 Heather Michelle Mollé
Recommended Citation
Mollé, Heather Michelle. "The growth of the quantum hyperbolic invariants of the figure eight knot." dissertation, University of Iowa, 2009.
http://ir.uiowa.edu/etd/409.