Totally knotted Seifert surfaces with accidental peripherals

Abstract. We show that if there exists an essential accidental surface in the knot exterior, then a closed accidental surface also exists. As its corollary, boundary slopes of accidental essential surfaces are integral or meridional. It is shown that an accidental incompressible Seifert surface is totally knotted. Example of satellite knot with arbitrarily high genus Seifert surfaces with acci-dental peripherals is given, and a Haken 3-manifold which contains a hyperbolic knot with an accidental incompressible Seifert surface is also given. 1