Classification of 3-bridge spheres of 3-bridge arborescent links

Yeonhee Jang

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arXiv · 1107.1112

Classification of 3-bridge spheres of 3-bridge arborescent links

Yeonhee Jang

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Abstract

In this paper, we give an isotopy classification of 3-bridge spheres of 3-bridge arborescent links, which are not Montesinos links. To this end, we prove a certain refinement of a theorem of J.S. Birman and H.M. Hilden on the relation between bridge presentations of links and Heegaard splittings of 3-manifolds. In the proof of this result, we also give an answer to a question by K. Morimoto on the classification of genus-2 Heegaard splittings of certain graph manifolds.

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Yeonhee Jang. 2011-07-05. Classification of 3-bridge spheres of 3-bridge arborescent links. https://arxiv.org/abs/1107.1112

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