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January, 2015 Knotted handle decomposing spheres for handlebody-knots
Atsushi ISHII, Kengo KISHIMOTO, Makoto OZAWA
J. Math. Soc. Japan 67(1): 407-417 (January, 2015). DOI: 10.2969/jmsj/06710407

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.

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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

Published: January, 2015
First available in Project Euclid: 22 January 2015

zbMATH: 1316.57005
MathSciNet: MR3304027
Digital Object Identifier: 10.2969/jmsj/06710407

Subjects:
Primary: 57M25

Keywords: decomposing sphere , handlebody-knot

Rights: Copyright © 2015 Mathematical Society of Japan

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Vol.67 • No. 1 • January, 2015
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