Title: Densities of Hyperbolic Cusp Invariants,
Abstract: We find that cusp densities of hyperbolic knots in the 3-sphere are dense in
[0,0.6826...] and those of links are dense in [0,0.853...]. We define a new
invariant associated with cusp volume, the cusp crossing density, as the ratio
between the cusp volume and the crossing number of a link, and show that cusp
crossing density for links is bounded above by 3.1263.... Moreover, there is a
sequence of links with cusp crossing density approaching 3. The least upper
bound for cusp crossing density remains an open question. For two-component
hyperbolic links, cusp crossing density is shown to be dense in the interval
[0,1.6923...] and for all hyperbolic links, cusp crossing density is shown to
be dense in [0, 2.120...].