The conformal structure on the cuspidal torus is usually called the "cusp shape."

See Adams, Hildebrand, Weeks Hyperbolic invariants of knots and links and McReynolds, Arithmetic cusp shapes are dense, for starters.

See also work on "geometric inflexibility" by Neumann and Reid.

Also check out the work of Marc Lackenby and Jessica Purcell.

The conformal structure on the cuspidal torus is usually called the "cusp shape."

See Adams, Hildebrand, Weeks Hyperbolic invariants of knots and links and McReynolds, Arithmetic cusp shapes are dense, for starters.

See also work on "geometric inflexibility" by Neumann and Reid.

Also check out the work of Marc Lackenby and Jessica Purcell.