Abstract
We show that a handlebody-knot whose exterior is boundary-irreducible has a unique maximal unnested set of knotted handle decomposing spheres up to isotopies and annulus-moves. As an application, we show that the handlebody-knots $6_{14}$ and $6_{15}$ are not equivalent. We also show that certain genus two handlebody-knots with a knotted handle decomposing sphere can be determined by their exteriors. As an application, we show that the exteriors of $6_{14}$ and $6_{15}$ are not homeomorphic.
Citation
Atsushi ISHII. Kengo KISHIMOTO. Makoto OZAWA. "Knotted handle decomposing spheres for handlebody-knots." J. Math. Soc. Japan 67 (1) 407 - 417, January, 2015. https://doi.org/10.2969/jmsj/06710407
Information
