Date of this Version
Sorsen, Rebecca. The Jones Polynomial of the Generalized Half-Twist. University of Nebraska-Lincoln. 2018.
The Jones Polynomial is a specific knot invariant that can yield extremely useful information; however, the Jones Polynomial is computationally complex. While computers can calculate the Jones Polynomial up to a certain complexity, we are interested in much larger, complex examples. Specifically, we will focus on a special class of knots with many twisted, parallel strands, called the generalized half twist. We will discuss the properties of the Kauffman bracket expansion of the generalized half twist and apply our findings to the Jones Polynomial.