Hyperbolic Invariants

For knots with a hyperbolic complement, there is a complete hyperbolic structure. For that structure, there is a maximal peripheral torus that is flat, that is, with an induced Euclidean structure.

Take the volume of the complete hyperbolic structure of the complement.

Maximal Cusp Volume
For the hyperbolic structure, there is a maximal peripheral torus that is flat, and it splits off the maximal cusp. The table gives the volume of that cusp.

Longitude and Meridian Length
The table gives the length of the longitude and meridian with respect to the hyperbolic structure.

Longitude and Meridian Translation
For the hyperbolic structure, the meridian and longitude lift to give translations of the universal cover of the torus, which can be identified with R2 with the standard metric. The table gives the translation vector associated to the longitude, normalized so that the vector has no y-component.

Other Short Geodesics
If there are other short curves on the torus, these are listed here. The notation gives the number of meridians and longitudes represented by the curve, along with its length.

The data is taken from Knotscape, which itself is using Snappea to compute the values, and orientation issues are still being checked.

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