论文标题
单极和Landau-Ginzburg型号
Monopoles and Landau-Ginzburg Models I
论文作者
论文摘要
这一系列论文的终点是为任何一对$（y，ω）$构建单极浮子同源性，其中$ y $是带有圆环边界的紧凑型3个manifold，$ω$是合适的封闭2型。在第一篇论文中，我们利用了仪表的Landau-Ginzburg模型的框架来解决（受扰动的）seiberg-Witten Moduli空间上的两个模型问题我们的第一个结果指出，$ \ mathbb {c} \timesς$上扰动方程的有限能量解决方案必然是微不足道的。第二个指出，在$ \ mathbb {h}^2 _+\timesς$上的小能量解决方案必然会在空间方向上呈指数级衰减。这些结果最终将导致第二篇论文中的紧凑定理。
The endpoint of this series of papers is to construct the monopole Floer homology for any pair $(Y,ω)$, where $Y$ is a compact oriented 3-manifold with toroidal boundary and $ω$ is a suitable closed 2-form. In the first paper, we exploit the framework of the gauged Landau-Ginzburg models to address two model problems for the (perturbed) Seiberg-Witten moduli spaces on either $\mathbb{C}\timesΣ$ or $\mathbb{H}^2_+\timesΣ$, where $Σ$ is any compact Riemann surface of genus $\geq 1$. Our first result states that finite energy solutions to the perturbed equations on $\mathbb{C}\timesΣ$ are necessarily trivial. The second states that small energy solutions on $\mathbb{H}^2_+\timesΣ$ necessarily have energy decaying exponentially in the spatial direction. These results will lead eventually to the compactness theorem in the second paper.
