Characterization of 3-punctured spheres in non-hyperbolic link exteriors (Q2315318)

This paper characterizes 3-component links in the 3-sphere whose exterior contains either an essential annulus or essential torus, as well as an essential thrice punctured sphere whose boundary components are non-meridional and have non-integral slopes. On a different but related question, the paper also considers the embeddability into the 3-sphere of a multibranched surface with 3 branching curves and with a single 3-punctured sphere sector whose covering degrees are greater than 1.