Monodromy action on unknotting tunnels in fiber surfaces

Abstract

In "Tunnel one, fibered links", the second author showed that the tunnel of a tunnel number one, fibered link can be isotoped to lie as a properly embedded arc in the fiber surface of the link. In this paper, we analyze how the arc behaves under the monodromy action, and show that the tunnel arc is nearly clean, with the possible exception of twisting around the boundary of the fiber.

28 pages, 16 figures; mistaken Corollary 4.2 removed, examples added, new application of Corollary 5.3 added, minor typos edited

References in corpus (4)

• Knot Floer homology detects fibred knots
• Fractional Dehn twists in knot theory and contact topology
• Cusp geometry of fibered 3-manifolds
• Minimal pseudo-Anosov translation lengths on the complex of curves

Cited by in corpus (1)

• Dehn surgery on complicated fibered knots in the 3-sphere