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Beyond the Tails of the Colored Jones Polynomial

In [2] 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 [8]. 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 [7].

Identiferoai:union.ndltd.org:LSU/oai:etd.lsu.edu:etd-07012016-104111
Date11 July 2016
CreatorsPeng, Jun
ContributorsDasbach, Oliver T, Koray, Faik A, Davidson, Mark G, Litherland, Richard A, Stoltzfus, Neal W
PublisherLSU
Source SetsLouisiana State University
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lsu.edu/docs/available/etd-07012016-104111/
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