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Caltech/USC/UCLA Joint Topology Seminar

Monday, November 5, 2018
4:00pm to 5:00pm
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Linde Hall 310
SW = Gr
Chris Gerig, Mathematics Department, Harvard University,
Whenever the Seiberg-Witten (SW) invariants of a 4-manifold X are defined, there exist certain 2-forms on X which are symplectic away from some circles. When there are no circles, i.e. X is symplectic, Taubes' ``SW=Gr'' theorem asserts that the SW invariants are equal to well-defined counts of J-holomorphic curves (Taubes' Gromov invariants). In this talk I will describe an extension of Taubes' theorem to non-symplectic X: there are well-defined counts of J-holomorphic curves in the complement of these circles, which recover the SW invariants. This ``Gromov invariant'' interpretation was originally conjectured by Taubes in 1995.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].