The SnapPy manifold database for plausibly slice knots

The PlausibleKnots database consists of those nontrivial prime knots with at most 19 crossings whose signature is 0 and whose Alexander polynomial satisfies the Fox-Milnor condition. The data on these 3.9 million knots takes up about 1.1G of disk space.

To install the latest version of this Python module, you can do:

python -m pip install plausible_knots

If you are using SageMath, replace this with:

sage -pip install plausible_knots

Please note this will take about a minute as it’s downloading 1.1G of raw data as part of the build_wheel step.

Assuming you have installed SnapPy into this Python, you can now start Python and do:

>>> import snappy
>>> import plausible_knots      # Skip if using SnapPy 3.3.2 or newer.
>>> len(snappy.PlausibleKnots)
3869541
>>> K = snappy.PlausibleKnots[100000]; K
17nh_1645806(0,0)
>>> K.volume()
24.3340174921580
>>> M = snappy.PlausibleKnots['19nh_045358315']
>>> M.identify()
[19nh_045358315(0,0)]

The raw data is available on the GitHub repository and archived on the Dataverse. This database was created as part of [Dunfield and Gong].