论文标题
拓扑4型具有4维基本组
Topological 4-manifolds with 4-dimensional fundamental group
论文作者
论文摘要
让$π$是满足Farrell-Jones猜想的一组，并假设$bπ$是4维庞加莱二元空间。我们考虑使用基本组$π$的拓扑，封闭，连接的歧管，其规范地图为$bπ$具有1度，并显示两个这样的歧管是s-cobordant，并且只有当它们的eproivariant交叉点是等值线的，并且它们具有相同的Kirby-Siebenmann Invariant。如果$π$从弗里德曼（Freedman）的意义上是好的，那么当且仅当它们是同质且具有相同的kirby--siebenmann不变时，就可以得出两个这样的流形。这表明在许多情况下，这表明了刚性的4个manifolds之间的刚度，在这些情况下，Borel的猜想预期刚度是刚性的，并且仅连接了刚性的僵硬，这是Freedman分类结果的结果。
Let $π$ be a group satisfying the Farrell-Jones conjecture and assume that $Bπ$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $π$ whose canonical map to $Bπ$ has degree 1 and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby-Siebenmann invariant. If $π$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby--Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel's conjecture, and simply connected manifolds where rigidity is a consequence of Freedman's classification results.
