Is there a special name for the prime knots that have a hyperbolic volume of 0.0? They have

For example $3_1$, $5_1$, $7_1$, $9_1$ from the Knot Table. Also it seems there is some relationship between these knots, which are odd, and some links that are even, like L6a3.

  • $\begingroup$ These are exactly prime knots/links whose exteriors are graph-manifolds. I do not think there is a special name. $\endgroup$ Dec 29, 2022 at 3:38
  • $\begingroup$ These knots are not hyperbolic (the ones you list are torus knots), so they don't really have hyperbolic volumes. $\endgroup$ Dec 31, 2022 at 1:02
  • $\begingroup$ A knot (or link) falls into exactly one of three categories: torus, satellite, or hyperbolic. Only the hyperbolic knots have a hyperbolic volume. So by convention, we say that the hyperbolic volumes of torus and satellite knots are zero. $\endgroup$
    – N. Owad
    Jan 9, 2023 at 13:50


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