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Seiberg-Witten and Gromov invariants for non-symplectic 4-manifolds


Speaker: Chris Gerig, UC Berkeley
Location: 1147 MSB
Start time: Tue, Jan 16 2018, 1:10PM

Whenever the Seiberg-Witten (SW) invariants of a closed oriented 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. This talk will involve contact forms and spin-c structures.