Additional Resources for Topics in Knot Theory

This page will contain some Python code to experiment with the constructions that we cover in class.

Week 2:
Here we can experiment with Bridge positions, Kauffman States and the Alexander polynomial. You will need the file alexander.py
Its use is explained in a pdf file Alexander.pdf
Click here to download all the files for Week 2.

A simple way is to use a Python shell: python, ipython, python3 or ipython3.
Using Python: Download alexander.py into a directory.
In the same directory start Python by typing python or python3.
In the python shell you can import the functions by typing from alexander import *
Then you can start experimenting, for example by typing Alexander(Torus(5,6)) or Alexander(Pretzel(-3,5,7)) or NumberOfKauffmanStates(Torus(5,9))

A modern (and interactive) way is to work in a Jupyter notebook (for that you need to have jupyter installed).
In this case download alexander.py and in the same directory type jupyter notebook
Then open the notebook Alexander.ipynb, or in a fresh notebook import alexander: from alexander import *

An alternative is to work in Google Colab.
Upload alexander.py and Alexander_Colab.ipynb to Google Drive.
Here you can use Google Colab to open and run Alexander_Colab.ipynb

Week 3:
The new functions include knot signature, knot determinant, Seifert algorithm, bounds for the Seifert genus and bigraded generators for knot Floer homology.
The usage is explained in a pdf file Week3.pdf
Click here to download all the files for Week 3.

Week 6:
The new functions include Kauffman Bracket, Jones polynomial, Khovanov Homology and the Khovanov Lee homology.
The usage is explained in a pdf file Week6.pdf
Click here to download all the files for Week 6.