Additional Resources for Topics in Knot Theory
This page will contain some Python code to experiment with the constructions that we cover in class.
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
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.
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.