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 w...

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Main Author:	Peng, Jun
Other Authors:	Dasbach, Oliver T
Format:	Others
Language:	en
Published:	LSU 2016
Subjects:	Mathematics
Online Access:	http://etd.lsu.edu/docs/available/etd-07012016-104111/

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spelling	ndltd-LSU-oai-etd.lsu.edu-etd-07012016-1041112016-07-12T03:51:03Z Beyond the Tails of the Colored Jones Polynomial Peng, Jun Mathematics 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]. Dasbach, Oliver T Koray, Faik A Davidson, Mark G Litherland, Richard A Stoltzfus, Neal W LSU 2016-07-11 text application/pdf http://etd.lsu.edu/docs/available/etd-07012016-104111/ http://etd.lsu.edu/docs/available/etd-07012016-104111/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached herein a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to LSU or its agents the non-exclusive license to archive and make accessible, under the conditions specified below and in appropriate University policies, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.
collection	NDLTD
language	en
format	Others
sources	NDLTD
topic	Mathematics
spellingShingle	Mathematics Peng, Jun Beyond the Tails of the Colored Jones Polynomial
description	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].
author2	Dasbach, Oliver T
author_facet	Dasbach, Oliver T Peng, Jun
author	Peng, Jun
author_sort	Peng, Jun
title	Beyond the Tails of the Colored Jones Polynomial
title_short	Beyond the Tails of the Colored Jones Polynomial
title_full	Beyond the Tails of the Colored Jones Polynomial
title_fullStr	Beyond the Tails of the Colored Jones Polynomial
title_full_unstemmed	Beyond the Tails of the Colored Jones Polynomial
title_sort	beyond the tails of the colored jones polynomial
publisher	LSU
publishDate	2016
url	http://etd.lsu.edu/docs/available/etd-07012016-104111/
work_keys_str_mv	AT pengjun beyondthetailsofthecoloredjonespolynomial
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Beyond the Tails of the Colored Jones Polynomial

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