Heegaard Floer Homology and Knot Surgeries

Heegaard Floer Homology and Knot Surgeries

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Margaret Doig, Princeton University
Fine Hall 314

Wallace and Lickorish showed that any 3-manifold can be realized as surgery on a link in S3; however, fifty years later, we still have a rather poor understanding of which manifolds can be constructed from surgery on a knot and which knots give these surgeries. For example, the Berge Conjecture attempts to list all knots which can give rise to a lens space. We will ask a slightly easier question, that of which spherical Seifert fibered spaces (aka spherical space forms) arise as knot surgeries. We will use an obstruction from Heegaard Floer theory, the "correction terms" assigned to a manifold and its associated spin^c structures. These terms can be calculated either from a knot surgery description of a manifold or from a description of it as a Seifert fibered space.