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Knot Floer Homology and the 4-ball Genus
Student-Run Geometry/Topology Seminar| Speaker: | Jennifer Hom, University of Pennsylvania |
| Location: | 2112 MSB |
| Start time: | Tue, Nov 3 2009, 12:10PM |
In 2003, Ozsvath and Szabo defined a knot invariant, tau, using the knot filtration on the Heegaard Floer complex, and showed that tau gives a lower bound on the 4-ball genus of the knot. In this talk, I will define tau, state some of its properties, and use these properties to prove that the 4-ball genus of the (p, q) torus knot is (p-1)(q-1)/2 (a conjecture of Milnor, originally proved in 1993 by Kronheimer and Mrowka using Donaldson's invariants).