Date of Award
4-1-2022
Document Type
Honors Thesis
Department
Mathematics
First Advisor
Anthony Bosman
Abstract
A link is a collection of circles embedded into 3-dimensional space. Pretzel links are an important family of links which comprises those links that fit a general form that includes many of the most common links. The strong fusion of a link joins two components of the link via a band and adds an unknotted circle about the band [4]; this naturally arises in the study of concordance and has been used to model biological phenomena such as site specific recombination in DNA [2]. Here we present a complete and original classification of those pretzel links which can be obtained by strong fusion. The primary tools we depend on are linking number and a dichromatic resolution of the link in which we conceive of the link as being colored with two colors and resolve crossings in such a way that respects those colors. Solving the classification problem in a number of subcases gives the general result.
Recommended Citation
Homan, Jonathan, "Classifying Pretzel Links Obtained by Strong Fusion" (2022). Honors Theses. 266.
https://digitalcommons.andrews.edu/honors/266
Subject Area
Pretzel links (Mathematics); Forms (Mathematics)
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.