The number of strings on essential tangle decompositions of a knot can be unbounded

Abstract

We construct an infinite collection of knots with the property that any knot in this family has $n$-string essential tangle decompositions for arbitrarily high $n$.

11 pages, 6 figures

Cited by in corpus (3)

• Knot exteriors with all possible meridional essential surfaces
• Infinitely many meridional essential surfaces of bounded genus in hyperbolic knot exteriors
• Knot exteriors with all compact surfaces of positive genus essentially embedded