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arXiv · 2009.09531

Relative Seiberg-Witten invariants and a sum formula

Mohammad Farajzadeh-Tehrani·Pedram Safari
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Abstract

We study relative Seiberg-Witten moduli spaces and define relative invariants for a pair $(X,\Sigma)$ consisting of a smooth, closed, oriented 4-manifold $X$ and a smooth, closed, oriented 2-dimensional submanifold $\Sigma\!\subset\!X$ with positive genus. These relative Seiberg-Witten invariants are meant to be the counterparts of relative Gromov-Witten invariants. We also obtain a sum formula (aka a product formula) that relates the SW invariants of a sum $X$ of two closed oriented 4-manifolds $X_1$ and $X_2$ along a common oriented surface $\Sigma$ with dual self-intersections to the relative SW invariants of $(X_1,\Sigma)$ and $(X_2,\Sigma)$. Our formula generalizes Morgan-Szab\'o-Taubes' product formula.

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Mohammad Farajzadeh-Tehrani, Pedram Safari. 2020-09-20. Relative Seiberg-Witten invariants and a sum formula. https://arxiv.org/abs/2009.09531

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