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3:00 pm Monday, November 30, 2009 Stulken Topology Seminar: Curves on surfaces and fixed point Floer homologyby Tim Perutz (University of Texas) in HB 423- A sequence of Lagrangian spheres in a symplectic manifold M of dimension 2n determines a 2n+2 dimensional symplectic manifold E as the total space of a Lefschetz fibration over the disc whose generic fiber is M. One can attempt to determine the symplectic and smooth invariants of E from this presentation. When n=1, one is then trying to compute 4-dimensional symplectic invariants from the combinatorics of curves on a surface. One such problem asks for a calculation of the Seiberg-Witten invariant, which is a class in a (generally unknown) Floer homology group associated with the boundary. I will report on ongoing work directed towards this problem. Specifically, it proves a conjecture of Seidel about the Floer homology of the monodromy of a Lefschetz fibration.
Submitted by shelly@rice.edu |