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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 |
Description
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.