论文标题
光滑4个manifolds的模量空间的同源不稳定
Homological instability for moduli spaces of smooth 4-manifolds
论文作者
论文摘要
我们证明，与任何程度的同源性的任何简单连接的封闭平滑的4个manifold的模量空间都失败，这与所有维度在所有维度上发生的事情$ \ neq 4 $不同。我们还检测到各种模量空间之间的同源差异，例如4个manifolds的拓扑和平滑模量空间，以及具有正标准曲率指标的4个manifolds的模量空间。为了证明这些结果，我们使用Seiberg-witten方程来构建一个新的4个模型家庭的特征类别，该类别不稳定，并检测到维度4中的平滑和拓扑类别之间的差异。
We prove that homological stability fails for the moduli space of any simply-connected closed smooth 4-manifold in any degree of homology, unlike what happens in all dimensions $\neq 4$. We detect also the homological discrepancy between various moduli spaces, such as topological and smooth moduli spaces of 4-manifolds, and moduli spaces of 4-manifolds with positive scalar curvature metrics. To prove these results, we use the Seiberg-Witten equations to construct a new characteristic class of families of 4-manifolds, which is unstable and detects the difference between the smooth and topological categories in dimension 4.
