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On hyperbolic 3-manifolds obtained by Dehn surgery on links.

Kim, Soo Hwan; Kim, Yangkok — 2010

International Journal of Mathematics and Mathematical Sciences

An irreducible Heegaard diagram of the real projective 3-space $P^{3}$ .

Im, Young Ho; Kim, Soo Hwan — 2000

International Journal of Mathematics and Mathematical Sciences

$θ$ -curves inducing two different knots with the same $2$ -fold branched covering spaces

Soo Hwan Kim; Yangkok Kim — 2003

Bollettino dell'Unione Matematica Italiana

For a knot $K$ with a strong inversion $i$ induced by an unknotting tunnel, we have a double covering projection $Π : S^{3} \to S^{3} / i$ branched over a trivial knot $Π (fix (i))$ , where $fix (i)$ is the axis of $i$ . Then a set $Π (fix (i) \cup K)$ is called a $θ$ -curve. We construct $θ$ -curves and the $Z_{2} \oplus Z_{2}$ cyclic branched coverings over $θ$ -curves, having two non-isotopic Heegaard decompositions which are one stable equivalent.

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Currently displaying 1 – 3 of 3

On hyperbolic 3-manifolds obtained by Dehn surgery on links.

An irreducible Heegaard diagram of the real projective 3-space P 3 .

θ -curves inducing two different knots with the same 2 -fold branched covering spaces

An irreducible Heegaard diagram of the real projective 3-space $P^{3}$ .

$θ$ -curves inducing two different knots with the same $2$ -fold branched covering spaces