Osaka Journal of Mathematics

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

Kai Ishihara

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Abstract

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

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

Dates
First available in Project Euclid: 19 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1266586792

Mathematical Reviews number (MathSciNet)
MR2666131

Zentralblatt MATH identifier
1195.57015

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

Citation

Ishihara, Kai. On tunnel number one links with surgeries yielding the 3-sphere. Osaka J. Math. 47 (2010), no. 1, 189--208. https://projecteuclid.org/euclid.ojm/1266586792


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References

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