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Applications of controlled surgery in dimension 4: Examples

机译：受控手术在第4维中的应用：示例

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摘要

The validity of Freedman's disk theorem is known to depend only on the fundamental group. It was conjectured that it fails for nonabelian free fundamental groups. If this were true then surgery theory would work in dimension four. Recently, Krushkal and Lee proved a surprising result that surgery theory works for a large special class of 4-manifolds with free nonabelian fundamental groups. The goal of this paper is to show that this also holds for other fundamental groups which are not known to be good, and that it is best understood using controlled surgery theory of Pedersen-Quinn-Ranicki. We consider some examples of 4-manifolds which have the fundamental group either of a closed aspherical surface or of a 3-dimensional knot space. A more general theorem is stated in the appendix.
机译：已知Freedman磁盘定理的有效性仅取决于基本组。据推测，这对于非阿贝尔自由基本团体而言是失败的。如果这是真的，那么手术理论将适用于第四维度。最近，克鲁什卡尔（Krushkal）和李（Lee）证明了一个令人惊讶的结果，即手术理论适用于带有自由非阿贝尔基本群的大型4类特殊流形。本文的目的是表明，这也适用于其他尚无良好基础的人群，并且最好使用Pedersen-Quinn-Ranicki的受控外科手术理论对其进行最佳理解。我们考虑一些4流形的例子，这些流形具有基本的非球面曲面或3维结空间。附录中列出了更一般的定理。

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