Osaka Journal of Mathematics

On tunnel number one links with surgeries yielding the 3-sphere

Kai Ishihara

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Gordon and Luecke showed that knots are determined by their complements. Therefore a non-trivial Dehn surgery on a non-trivial knot does not yield the 3-sphere. But the situation for links is different from that for knots. Berge constructed some examples of Dehn surgeries of 2-component links yielding the 3-sphere with interesting properties. By extending Berge's example, we construct infinitely many examples of tunnel number one links in the 3-sphere, such that their components are non-trivial, and that non-trivial Dehn surgeries on them yield the 3-sphere.

Article information

Osaka J. Math., Volume 47, Number 1 (2010), 189-208.

First available in Project Euclid: 19 February 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx]


Ishihara, Kai. On tunnel number one links with surgeries yielding the 3-sphere. Osaka J. Math. 47 (2010), no. 1, 189--208.

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