Knotted handle decomposing spheres for handlebody-knots

Atsushi Ishii; Kengo Kishimoto; Makoto Ozawa

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arXiv · 1211.4458

Knotted handle decomposing spheres for handlebody-knots

Atsushi Ishii·Kengo Kishimoto·Makoto Ozawa

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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 some 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.

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BibTeX RIS

Atsushi Ishii, Kengo Kishimoto, Makoto Ozawa. 2012-11-19. Knotted handle decomposing spheres for handlebody-knots. https://arxiv.org/abs/1211.4458

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