On non almost-fibered knots
arXiv:2104.00039
Abstract
An almost-fibered knot is a knot whose complement possesses a circular thin position in which there is one and only one weakly incompressible Seifert surface and one incompressible Seifert surface. Infinite examples of almost-fibered knots are known. In this article, we show the existence of infinitely many hyperbolic genus one knots that are not almost-fibered.
arXiv admin note: text overlap with arXiv:1812.06930 by other authors