The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval $[0, v_{oct}]$ $[0, v_{oct}]$ . We construct sequences of alternating knots whose volume and determinant densities both converge to any $x \in [0, v_{oct}]$ $x \in [0, v_{oct}]$ . We also investigate the distributions of volume and determinant densities for hyperbolic rational links, and establish upper bounds and density results for these invariants.

Keywords:

AMSC: 57M25, 57M50

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