论文标题
相对Seiberg-intent的不变性和总和公式
Relative Seiberg-Witten invariants and a sum formula
论文作者
论文摘要
我们研究相对的Seiberg-Witten模量空间，并为一对$（x，σ）$定义相对不变性，由光滑，封闭，定向的4-manifold $ x $和平滑，封闭，定向的二维子手法$σ\！\！这些相对的Seiberg-witten不变性是相对Gromov-Witten不变的对应物。我们还获得了一个总和公式（又称一个产品配方），该公式将两个与$ x_1 $ x_1 $ x_1 $和$ x_2 $的$ x $ x $ x $ x $ x $ x $ x $ x x $ x x $ x_1 $和$ x_2 $相关联，沿着普通定向的表面$σ$与$（x_1，σ）$（x_1，σ）$和$（x_2，x_2，x_2，x_2，c）相对自我交往。我们的公式概括了Morgan-Szabó-Taubes的产品配方。
We study relative Seiberg-Witten moduli spaces and define relative invariants for a pair $(X,Σ)$ consisting of a smooth, closed, oriented 4-manifold $X$ and a smooth, closed, oriented 2-dimensional submanifold $Σ\!\subset\!X$ 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 $Σ$ with dual self-intersections to the relative SW invariants of $(X_1,Σ)$ and $(X_2,Σ)$. Our formula generalizes Morgan-Szabó-Taubes' product formula.
