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Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.
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A question on (1,1) bridge Knot
Hi, everyone. I am interested in the complement of (1,1) bridge knot in a lens space, $S^{3}$. Is there one (1,1) bridge knot in $S^{3}$ or lens space such that its complement is
hyperbolic?
Note …
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Getting surgery link from Heegaard splitting
I believe the following paper is what you need.
A PROOF OF LICKORISH AND WALLACE’S THEOREM
http://arxiv.org/pdf/1306.1376.pdf