The component number of a twisted torus link
Michelle S. Berry
Goucher College
Victoria Diaz
Florida International University
Brandy Doleshal
Sam Houston State University
Taylor Martin
Sam Houston State University
Emily T. Winn
College of the Holy Cross
http://orcid.org/0000-0001-6759-5406
Max Zhou
Indiana University Bloomington
Abstract
A link is a smooth embedding of a finite number of disjoint copies of S^1 into S^3. Links of one component are known as knots. We are particularly interested in twisted torus links, as no complete classification of them currently exists. Specifically, we are interested in finding ways to determine the number of components in a twisted torus link. Twisted torus links of one component are especially interesting because there exist more ways to classify knots than there are ways to classify links. In this paper, we will examine patterns in the parameters of a twisted torus link that reveal general and specific information about components.
