Hyperbolic Knots with a Large Number of Disjoint Minimal Genus Seifert Surfaces

Abstract

It is known that any genus one hyperbolic knot in the 3-dimensional sphere admits at most seven mutually disjoint and mutually non-parallel genus one Seifert surfaces. In this note, it is shown that for any integers $g>1$ and $n>0$, there is a hyperbolic knot of genus $g$ in the 3-dimensional sphere which bounds $n$ mutually disjoint and mutually non-parallel genus $g$ Seifert surfaces.