Subgroup separability of the figure 8 knot group

Abstract

It is shown that the fundamental groups of certain non-positively curved 2-complexes have the property that their quasiconvex subgroups are the intersections of finite index subgroups.

As a consequence, every geometrically finite subgroup of the figure 8 knot group is the intersection of finite index subgroups. The same result holds for many other prime alternating link groups.