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Heegaard Splittings and the Pants ComplexGeometry/Topology
|Speaker:||Jesse Johnson, UC Davis|
|Start time:||Wed, Jun 1 2005, 4:10PM|
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.