The head and tail conjecture for alternating knots

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2012

Author dc:creator

• Armond, Cody

• knot theory
• colored Jones polynomial
• skein theory
• head and tail
• adequate links

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-07032012-165733
https://repository.lsu.edu/gradschool_dissertations/1122

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-2121