Identifier
etd-07032012-165733
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
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.
Date
2012
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Armond, Cody, "The head and tail conjecture for alternating knots" (2012). LSU Doctoral Dissertations. 1122.
https://repository.lsu.edu/gradschool_dissertations/1122
Committee Chair
Dasbach, Oliver
DOI
10.31390/gradschool_dissertations.1122