Journal of the Mathematical Society of Japan

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 [3] 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 [23] on the classification of genus-2 Heegaard splittings of certain graph manifolds.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 1 (2013), 97-136.

Dates
First available in Project Euclid: 24 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1359036450

Digital Object Identifier
doi:10.2969/jmsj/06510097

Mathematical Reviews number (MathSciNet)
MR3034400

Zentralblatt MATH identifier
1275.57011

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M12: Special coverings, e.g. branched

Keywords
3-bridge spheres arborescent links

Citation

JANG, Yeonhee. Classification of 3-bridge spheres of 3-bridge arborescent links. J. Math. Soc. Japan 65 (2013), no. 1, 97--136. doi:10.2969/jmsj/06510097. https://projecteuclid.org/euclid.jmsj/1359036450


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References

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