Simple, small knots in handlebodies (Q1886718)

For a handlebody of any genus, the authors construct a simple, small knot. This means that the knot complement is irreducible, boundary-irreducible, anannular, toroidal and contains no essential closed surface. In fact, such a knot is hyperbolic. The result may be related to Lopez's conjecture claiming that every closed small \(3\)-manifold contains a small knot [\textit{L. M. Lopez}, Math. Z. 212, No. 1, 123--139 (1993; Zbl 0789.57009)]. For example, in the \(3\)-sphere, torus knots, \(2\)-bridge knots and links, Montesinos knots with length three and the Borromean rings are known to be small.