论文标题
从$ \ mathrm {pin}^{ - }（2）$ - monopole对光滑的4个manifolds家族的限制
Constraints on families of smooth 4-manifolds from $\mathrm{Pin}^{-}(2)$-monopole
论文作者
论文摘要
Baraglia使用Seiberg-on-on-on-nonopole方程式，最近证明，对于大多数简单连接的封闭平滑$ 4 $ - manifolds $ x $，夹杂物$ \ mathrm {diff}（x）\ hookrightArrow \ hookrightarrow \ mathrm {homeo}（homeo}（x）（x）$不是弱同型等值。在本文中，我们使用$ \ mathrm {pin}^{ - }（2）$ - monopole方程来概括Baraglia的结果。我们还提供了$ 4 $ -Manifolds $ x $的新示例，其中$π_{0}（\ Mathrm {diff}（x））\ toπ_{0}（\ Mathrm {homeo}（x）（x））$不是过度的。
Using the Seiberg-Witten monopole equations, Baraglia recently proved that for most of simply-connected closed smooth $4$-manifolds $X$, the inclusions $\mathrm{Diff}(X) \hookrightarrow \mathrm{Homeo}(X)$ are not weak homotopy equivalences. In this paper, we generalize Baraglia's result using the $\mathrm{Pin}^{-}(2)$-monopole equations instead. We also give new examples of $4$-manifolds $X$ for which $π_{0}(\mathrm{Diff}(X)) \to π_{0}(\mathrm{Homeo}(X))$ are not surjections.
