Dehn surgeries on knots which yield lens spaces and genera of knots

Details Dehn surgeries on knots which yield lens spaces and genera of knots Dehn surgeries on knots which yield lens spaces and genera of knots

1999-02-26

arxiv.org/abs/math/9902157v1

Mathematics

Geometric Topology

20 pages, 6 figures

Scientific paper

10.1017/S0305004100004692

Let $K$ be a hyperbolic knot in the 3-sphere. If $r$-surgery on $K$ yields a lens space, then we show that the order of the fundamental group of the lens space is at most $12g-7$, where $g$ is the genus of $K$. If we specialize to genus one case, it will be proved that no lens space can be obtained from genus one, hyperbolic knots by Dehn surgery. Therefore, together with known facts, we have that a genus one knot $K$ admits Dehn surgery yielding a lens space if and only if $K$ is the trefoil.

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