论文标题
Codimension-3 Riemannian Foliation的Monopole浮子同源性
Monopole Floer homology for codimension-3 Riemannian foliation
论文作者
论文摘要
在本文中，我们对Seiberg-Witten理论进行了系统的研究，该理论涉及封闭式歧管$ M $，并带有Codimension- $ 3 $面向的Riemannian Foliation $ f $。在某种拓扑状态下，我们构建基本的seiberg-intent不变性和单极浮子同源物$ \ bar {hm}（m，f，f，\ \ mfs;γ），〜\ hat {hm}（m，f，f，\ mfs;γ），， 〜\ widecheck {hm}（m，f，\ mfs;γ）$，对于每个横向\ spinc结构$ \ mfs $，其中$γ$是一个完整的本地系统。我们将证明这些同源性独立于捆绑式度量和通用扰动。基本的单极浮子同源物与流形的基本单极同源物之间的主要区别在于，必须在基本的单极浮子同源物上使用Novikov环。
In this paper, we give a systematic study of Seiberg-Witten theory on closed oriented manifold $M$ with codimension-$3$ oriented Riemannian foliation $F$. Under a certain topological condition, we construct the basic Seiberg-Witten invariant and the monopole Floer homologies $\bar{HM}(M,F,\mfs;Γ),~\hat{HM}(M,F,\mfs;Γ), ~\widecheck{HM}(M,F,\mfs;Γ)$, for each transverse \spinc structure $\mfs$, where $Γ$ is a complete local system. We will show that these homologies are independent of the bundle-like metric and generic perturbation. The major difference between the basic monopole Floer homologies and the ones on manifolds is the necessity to use the Novikov ring on basic monopole Floer homologies.
