Doctor of Philosophy (PhD)
In  Armond showed that the heads and tails of the colored Jones polynomial exist for adequate links. This was also shown independently by Garoufalidis and Le for alternating links in . Here we study coefficients of the "difference quotient" of the colored Jones polynomial. We begin with the fundamentals of knot theory. A brief introduction to skein theory is also included to illustrate those necessary tools. In Chapter 3 we give an explicit expression for the first coefficient of the relative difference. In Chapter 4 we develop a formula of t_2, the number of regions with exactly 2 crossings in the diagram of a link, for a specific class of alternating links, and then improve with this result the upper bound of the volume for a hyperbolic alternating link which Dasbach and Tsvietkova gave in the coefficients of the colored Jones polynomial in .
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Peng, Jun, "Beyond the Tails of the Colored Jones Polynomial" (2016). LSU Doctoral Dissertations. 2227.
Dasbach, Oliver T