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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| Format: | Others |
| Language: | en |
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LSU
2016
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| Online Access: | http://etd.lsu.edu/docs/available/etd-07012016-104111/ |
| Summary: | 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]. |
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