Title : Dehn surgery and $(1, 1)$-knots in lens spaces
Speaker : Toshio Saito (Osaka University)
Abstract :

It is one of the unsolved problems to decide the knots in the $3$-sphere which have non-trivial Dehn surgery yielding lens spaces. The concept of double-primitive knots is introduced by Berge, and he gave some families of knots satisfying the above. It is conjectured that Berge's list is complete. Let $K$ be a double-primitive knot in the $3$-sphere and $M$ a lens space obtained by Dehn surgery on $K$. Then we can naturally find the dual knot $K'$ in $M$. It is expected that $K'$ is a $(1,1)$-knot in $M$. In this talk, we give some necessary conditions for $(1,1)$-knots in lens spaces which have non-trivial Dehn surgery yielding the $3$-sphere.

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