Isaac Sundberg

KhNoDe

Khovanov homology Nontriviality Detector (download | github | readme)
This Python program allows the user to determine nontriviality of a Khovanov homology class by testing if the representative chain is a boundary in the Khovanov chain complex. The program also will verify that the representative chain is a cycle.
A method for finding nontrivial Khovanov homology classes is under development.

Directions

Please consult the Read Me for details about the program, installation, usage, citations, and a running to-do list. Some of this information is summarized here for easy access.
Installation
Download the current version as khnode.py and save to a local folder. Install the latest version of Python, and then install the SymPy module. Execute the khnode.py file from the command line.
Alternatively, one can download each class from the current version's github page and piece together a python project and compile with a preferred IDE (we use PyCharm)
Citation
Isaac Sundberg, KhNoDe, a program for determining nontriviality of Khovanov homology classes, imsundberg.github.io/khnode, 2023.
Contact
Please direct feedback, bug reports, and questions to sundberg@mpim-bonn.mpg.de

Version History

KhNoDe 2 (download | github | readme)
January 2023, current version
  • Requirements: Windows 10, Python 3.9 or later (running SymPy)
  • Update: implements SymPy (replaces SageMath); implements new Tkinter GUI
  • Plans: continued GUI improvement; option to search for nontrivial classes for a given diagram
KhNoDe 1 (download)
April 2022
  • Requirements: Windows 10, SageMath, Python 3.9 or later
  • No longer supported