On non almost-fibered knots

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.

Figures (13)

• Figure 1:
• Figure 2:
• Figure 3:
• Figure 4:
• Figure 5:

Theorems & Definitions (34)

• Theorem 1
• Theorem 2: F. Manjarrez-Gutiérrez
• Theorem 3: F. Manjarrez-Gutiérrez
• Lemma 1
• Theorem 4
• proof
• Theorem 5
• proof
• Lemma 2
• proof