This repository contains calculations for the paper A new concordance homomorphism from Khovanov homology, namely the universal Khovanov homology and S-invariant (defined in the above-mentioned paper) of the 3n-twisted positive Whitehead doubles of the (2,2n+1)-torus knots for 0 < n < 13.
The python-script whitehead_torus.py generates PD Code for twisted Whitehead doubles of torus knots. Internally, it uses Morse Code and the script morse2pd.py to convert Morse Code to PD Code (the latter script file was originally written for a different project). The resulting PD Codes are saved in the file PD_Codes.txt.
Then, using those PD codes, the program khoca is used to calculate universal (a.k.a. equivariant) Khovanov homology of the Whitehead doubles.
Finally, the program homca is used to extract the S-invariant from the output of khoca. For this purpose, the output of khoca needs to be slightly reformatted. This reformatted output is contained in the file _n_-formatted.txt for 0 < n < 13.
The file homca.ipynb is a Jupyter Notebook file containing a slight modification of the homca sage code, as well as the calculations of the S-invariant of the Whitehead doubles.
The file homca.html contains a copy of the Jupyter Notebook, which can be directly viewed in the browser.