No abstract

Let Γ be a hyperbolic link in a Seifert-fibered space N over a surface S of negative Euler characteristic. When Γ is stratified, as defined in this paper, we show that the volume of N \ Γ is quasi-isometric to expressions involving distances in the pants graph. When S is a punctured torus or a four punctured sphere and N = P T 1 (S), we show that the canonical lift Γ of a filling collection Γ of essential simple closed curves is always stratified and that the volume is quasi-isometric to curve complex distance. Lastly, we given large families of stratified hyperbolic canonical links in P T 1 (S).