论文标题
原孔和单极浮子同源性
Protocorks and monopole Floer homology
论文作者
论文摘要
我们介绍并研究了一类带有边界的紧凑型4个manifolds，它们称为原始的。任何异国情调的简单连接的封闭的4个manifolds都与原始扭曲相关，此外，任何软木都由原始的软木支撑。我们证明了对扭曲前后的原始seiberg-onginter不变性的定理，以及在原始边界的浮子同源性上分裂的定理。作为推论，我们改善了Morgan和Szabó的定理，介绍了Seiberg-witten不变性具有上限的变化，该变化仅取决于数据的拓扑。此外，我们概括了这样的结果，即仅减少软木边界的浮动同源性有助于在软木扭转下变成塞伯格（Seiberg）编织的不变性剂，从而更通用的切割和粘贴操作，其中所涉及的零件是$ 1 $连接的，并且与边界相对。
We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a theorem on the relative Seiberg-Witten invariants of a protocork before and after twisting and a splitting theorem on the Floer homology of protocork boundaries. As a corollary we improve a theorem by Morgan and Szabó regarding the variation of Seiberg-Witten invariants with an upper bound which depends only on the topology of the data. Moreover, we generalize the result that only the reduced Floer homology of a cork boundary contributes to the variation of the Seiberg-Witten invariants under a cork twist to more general cut and paste operations where the pieces involved are $1$-connected and homeomorphic relative to the boundary.
