Differential Geometry Seminar
I will introduce relative Seiberg-Witten (or SW) moduli spaces for an arbitrary pair $(X,S)$ of a closed oriented 4-manifold $X$ and a closed oriented 2-dimensional submanifold $S$ in $X$ with positive genus. Using these moduli spaces, we obtain an SW 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 $S$ with dual self-intersections to the relative SW invariants of $(X_1,S)$ and $(X_2,S)$. This formula generalizes Morgan-Szabo-Taubes' product formula. This is joint work with Pedram Safari.