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arXiv · 1310.7314

On Heegaard splittings of knot exteriors with tunnel number degenerations

Kanji Morimoto
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Abstract

Let $K_1, K_2$ be two knots with $t(K_1)+t(K_2)>2$ and $t(K_1 # K_2)=2$. Then, in the present paper, we will show that any genus three Heegaard splittings of $E(K_1 # K_2)$ is strongly irreducible and that $E(K_1 # K_2)$ has at most four genus three Heegaard splittings up to homeomorphism. Moreover, we will give a complete classification of those four genus three Heegaard splittings and show unknotting tunnel systems of knots $K_1 # K_2$ corresponding to those Heegaard splittings.

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Kanji Morimoto. 2013-10-28. On Heegaard splittings of knot exteriors with tunnel number degenerations. https://arxiv.org/abs/1310.7314

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