link-khovanov

Compute distinct integral Khovanov homologies across component orientations of a link.

Installation

pip install link-khovanov

Usage example

from link_khovanov import link_khovanov

hopf = [[2, 3, 1, 4], [4, 1, 3, 2]]
for value in link_khovanov(hopf):
    print(value)

Algorithm

The PD component graph is decomposed into oriented cycles. One global orientation is fixed because reversing every component simultaneously is redundant; the remaining 2^(n-1) orientation representatives are evaluated and duplicate homology strings are removed. Computation is delegated in batches to the Khovanov backend to avoid starting a new compiler or process for every orientation.

Input conventions

A PD code is represented as a list of four-entry crossings. Arc labels normally occur exactly twice. Public functions validate inputs and return new values rather than mutating caller-owned data unless their API explicitly says otherwise.

External software

• A C++14 compiler is required by the Khovanov backend on first use.
• No Java runtime is required.

Development

Run examples and package checks before release. Python packages require Python 3.10 or newer. Build PyPI artifacts with:

poetry check
poetry build

License

MIT. See LICENSE.