论文标题
Monopoles和Landau-Ginzburg型号III：胶合定理
Monopoles and Landau-Ginzburg Models III: A Gluing Theorem
论文作者
论文摘要
这是本系列的第三篇论文。在\ cite {wang20}中，我们定义了任何一对$（y，ω）$的单极浮子同源性，其中$ y $是带有圆环边界的紧凑型3个序列，$ω$是合适的封闭的2型封闭式2型，可将其视为装饰。在本文中，当两个这样的3个manifolds沿着它们的共同边界适当地粘合，假设$ \ partial y $已断开连接，并且$ω$很小，但对$ \ partial y $却不呈危险，我们就为此浮子同源性建立了一个胶合定理。 作为应用，我们构建了一个单极浮子2函数和广义的恢复图。使用Kronheimer-Mrowka和Ni的结果，可以证明，对于任何不可约的3个manifold $ y $，该平面同源性检测到$ h_2（y，\ partial y; \ partial y; \ mathbb {r}）$ and $ y $ $ y $ $ y $ $ h_2（y，\ partial y; \ partial y; \ mathbb {r}）。最后，我们表明我们的构造恢复了封闭的3个manifold内部的任何链接的单极链接浮子同源性。
This is the third paper of this series. In \cite{Wang20}, we defined 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 viewed as a decoration. In this paper, we establish a gluing theorem for this Floer homology when two such 3-manifolds are glued suitably along their common boundary, assuming that $\partial Y$ is disconnected, and $ω$ is small and yet non-vanishing on $\partial Y$. As applications, we construct a monopole Floer 2-functor and the generalized cobordism maps. Using results of Kronheimer-Mrowka and Ni, it is shown that for any such 3-manifold $Y$ that is irreducible, this Floer homology detects the Thurston norm on $H_2(Y,\partial Y;\mathbb{R})$ and the fiberness of $Y$. Finally, we show that our construction recovers the monopole link Floer homology for any link inside a closed 3-manifold.
