| Type of Document |
Dissertation |
| Author |
Armond, Cody
|
| URN |
etd-07032012-165733 |
| Title |
The Head and Tail Conjecture for Alternating Knots |
| Degree |
Doctor of Philosophy (Ph.D.) |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Dasbach, Oliver |
Committee Chair |
| Davidson, Mark |
Committee Member |
| Gilmer, Patrick |
Committee Member |
| Hoffman, Jerome |
Committee Member |
| Litherland, Richard |
Committee Member |
| Peng, Lu |
Dean's Representative |
|
| Keywords |
- knot theory
- colored Jones polynomial
- skein theory
- head and tail
- adequate links
|
| Date of Defense |
2012-03-27 |
| Availability |
unrestricted |
Abstract
The colored Jones polynomial is an invariant of knots and links, which produces a sequence of Laurent polynomials. In this work, we study new power series link invariants, derived from the colored Jones polynomial, called its head and tail. We begin with a brief survey of knot theory and the colored Jones polynomial in particular. In Chapter 3, we use skein theory to prove that for adequate links, the n-th leading coefficient of the N-th colored Jones polynomial stabilizes when viewed as a sequence in N. This property allows us to define the head and tail for adequate links. In Chapter 4 we show a class of knots with trivial tail, and in Chapter 5 we develop techniques to calculate the head and tail for various knots and links using a graph derived from the link diagram.
|
| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
|
| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
armond_diss.pdf |
527.24 Kb |
00:02:26 |
00:01:15 |
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