  We study invariant Seifert surfaces for strongly invertible knots, and prove
that the gap between the equivariant genus (the minimum of the genera of
invariant Seifert surfaces) of a strongly invertible knot and the (usual) genus
of the underlying knot can be arbitrary large. This forms a sharp contrast with
Edmonds' theorem that every periodic knot admits an invariant minimal genus
Seifert surface. We also prove variants of Edmonds' theorem, which are useful
in studying invariant Seifert surfaces for strongly invertible knots.
