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The disjoint curve property
Geometry/Topology| Speaker: | Saul Schleimer, U of Illinois, Chicago |
| Location: | 693 Kerr |
| Start time: | Wed, Oct 29 2003, 4:10PM |
Description
As defined by Thompson, a Heegaard splitting H has the disjoint curve
property if there is a triple of essential curves a, b, c in H where,
first, a is disjoint from b and b is disjoint from c and, second, a and c
bound disks on opposite sides of H. We'll prove that if H has
sufficiently high genus (with respect to the ambient three-manifold) then
H has the disjoint curve property. The proof is technical and relies
extensively on normal surface theory.