Knotted handle decomposing spheres for handlebody-knots

2012/11/19 by Ishii, Atsushi, Kishimoto, Kengo, Ozawa, Makoto · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1211.4458

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 6₁₄ and 6₁₅ 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 6₁₄ and 6₁₅ are not homeomorphic.

Cited by

• A table of genus two handlebody-knots with seven crossings
• Handlebody-knots obtained by tangle replacement

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