Cabling sequences of tunnels of torus knots

Abstract

In previous work, we developed a theory of tunnels of tunnel number $1$ knots in $S^3$. It yields a parameterization in which each tunnel is described uniquely by a finite sequence of rational parameters and a finite sequence of $0$s and $1$s, that together encode a procedure for constructing the knot and tunnel. In this paper we calculate these invariants for all tunnels of torus knots