论文标题
集中在三个序列方程的两翼seiberg-witten方程的局部解决方案
Concentrating Local Solutions of the Two-Spinor Seiberg-Witten Equations on 3-Manifolds
论文作者
论文摘要
给定一个紧凑的3个manifold $ y $和A $ \ MATHBB Z_2 $ -HARMONIC SPINOR $（\ MATHCAL Z_0，A_0，φ_0）$，带有单数集$ \ Mathcal Z_0 $，本文构建了一家本地解决方案，以构建了$ ^ 0（$Å的$ε的$ seiberg-witten equartiation $ gibers）。 $ \ Mathcal Z_0 $。这些解决方案集中在某种意义上是$ \ Mathcal z_0 $ n of $ l^2 $ norm norm norm z_0 $差异为$ε\ to 0 $，并且在重新归一化之后，它们将本地汇聚到原始的$ \ Mathbb Z_2 $ -Harmonic Spinor。在本文的续集中，这些模型解决方案用于粘合构造中，表明任何$ \ mathbb z_2 $ harmonic Spinor满足了一些轻度假设，这是一个两旋式Seiberg-witter解决方案的限制。
Given a compact 3-manifold $Y$ and a $\mathbb Z_2$-harmonic spinor $(\mathcal Z_0, A_0,Φ_0)$ with singular set $\mathcal Z_0$, this article constructs a family of local solutions to the two-spinor Seiberg-Witten equations parameterized by $ε\in (0,ε_0)$ on tubular neighborhoods of $\mathcal Z_0$. These solutions concentrate in the sense that the $L^2$-norm of the curvature near $\mathcal Z_0$ diverges as $ε\to 0$, and after renormalization they converge locally to the original $\mathbb Z_2$-harmonic spinor. In a sequel to this article, these model solutions are used in a gluing construction showing that any $\mathbb Z_2$-harmonic spinor satisfying some mild assumptions arises as the limit of a family of two-spinor Seiberg-Witten solutions on $Y$.
