# Mathematics Colloquia and Seminars

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### Bounds on Dehn filling and handle addition

**Geometry/Topology**

Speaker: | Ian Agol, Mathematics, UC Davis |

Location: | 693 Kerr |

Start time: | Wed, Oct 21 1998, 4:10PM |

One endeavor in 3-manifold topology is to understand the topology of Dehn fillings on knot complements. Call a manifold hyperbolike if it is irreducible, has infinite fundamental group, and has no Z+Z subgroup. The geometrization conjecture would imply that hyperbolike manifolds are hyperbolic. I'll show that the number of non-hyperbolike Dehn fillings on a hyperbolic knot complement is 12. The techniques also show that there are at most finitely many handle additions to an acylindrical manifold which are not hyperbolic and acylindrical.