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Surgery formulas for Seiberg-Witten invariants and family Seiberg-Witten invariants

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arxiv 2411.10392 v1 pith:WH5FZWDP submitted 2024-11-15 math.GT

Haochen Qiu This is my paper · ORCID
classification math.GT
keywords surgeryseiberg-witteninvariantsformulasfamiliesformulaspaceclass
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abstract

We prove a surgery formula for the ordinary Seiberg-Witten invariants, and surgery formulas for the families Seiberg-Witten invariants of families of $4$-manifolds obtained through fibrewise surgery. Our formula expresses the Seiberg-Witten invariants of the manifold after the surgery, in terms of the original Seiberg-Witten moduli space cut down by a cohomology class in the configuration space. We use these surgery formulas to study how a surgery can preserve or produce exotic phenomena.

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  1. Irreducible 4-manifolds can admit exotic diffeomorphisms

    math.GT 2024-12 accept novelty 7.0 of 10

    The authors construct the first examples of irreducible closed 4-manifolds admitting exotic diffeomorphisms, using a families Seiberg-Witten constraint and explicit lattice automorphisms.

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