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March 2010 On tunnel number one links with surgeries yielding the 3-sphere
Kai Ishihara
Osaka J. Math. 47(1): 189-208 (March 2010).

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.

Citation

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Kai Ishihara. "On tunnel number one links with surgeries yielding the 3-sphere." Osaka J. Math. 47 (1) 189 - 208, March 2010.

Information

Published: March 2010
First available in Project Euclid: 19 February 2010

zbMATH: 1195.57015
MathSciNet: MR2666131

Subjects:
Primary: 57M25
Secondary: 57N10

Rights: Copyright © 2010 Osaka University and Osaka City University, Departments of Mathematics

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Vol.47 • No. 1 • March 2010
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