Knot exteriors with all compact surfaces of positive genus essentially embedded

Abstract

It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components.

13 pages, 10 figures. To appear in Topology and its Applications

References in corpus (4)

• Prime knot complements with meridional essential surfaces of arbitrarily high genus
• The number of strings on essential tangle decompositions of a knot can be unbounded
• Knot exteriors with all possible meridional essential surfaces
• Infinitely many meridional essential surfaces of bounded genus in hyperbolic knot exteriors