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Heegaard Splittings and the Pants Complex
Geometry/Topology| Speaker: | Jesse Johnson, UC Davis |
| Location: | 693 Kerr |
| Start time: | Wed, Jun 1 2005, 4:10PM |
Description
Hempel has defined a measure of complexity for Heegaard
splittings based on distances in a graph called the curve complex. I
will define a similar notion based on the pants complex, a graph
defined by Hatcher and Thurston. This new notion of complexity proves
to depend more on the topology of the manifold than on the particular
Heegaard splitting. Specifically, for any infinite sequence of
stabilizations, the distance minus the genus converges to a non-trivial
integer which depends only on the manifold.