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Title:
Seiberg-Witten and Gromov invariants in the presence of near-symplectic forms
Speaker:
Abstract:
Whenever the Seiberg-Witten invariants of a closed oriented 4-manifold X are defined, there exist self-dual harmonic 2-forms on X which vanish along a disjoint union of circles and are symplectic elsewhere. When there are no zero-circles, i.e. X is symplectic, Taubes' "SW=Gr" theorem asserts that these 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, i.e. I will describe well-defined counts of J-holomorphic curves in the complement of these zero-circles, which recover the Seiberg-Witten invariants. This "Gromov invariant" interpretation was originally conjectured by Taubes in 1995. This talk will involve embedded contact homology (ECH).
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