# Mathematics Colloquia and Seminars

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### Genera of knots and Lens spaces yielded by Dehn surgery on knots

**Colloquium**

Speaker: | Hiroshi Goda, Kobe University and UC Davis |

Location: | 693 Kerr |

Start time: | Wed, Jan 13 1999, 4:10PM |

This is recent joint work with Masakazu Teragaito. There are many studies on the problem of what kind of a knot admits Dehn surgery yielding a lens space, or the problem of what lens space can be obtained by Dehn surgery on knots. We will focus on the genera of knots, and we give an estimate of the order of the fundamental group of a lens space obtained by Dehn surgery on a knot, by using the labeled graphs on a Seifert surface and a Heegaard torus of a lens space. In particular, we will prove that a genus one knot K admits Dehn surgery yielding a lens space if and only if K is the trefoil.