It is shown that any finite list of smooth, closed, simply-connected 4-manifolds that are homeomorphic to a given one X can be obtained by removing a single compact contractible submanifold (or cork) from X, and then regluing it by powers of a boundary diffeomorphism. Furthermore, by allowing the cork to be noncompact, the collection of all the smooth manifolds homeomorphic to X can be obtained in this way. The existence of a universal noncompact cork is also established.

中文翻译：

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高阶软木塞

结果表明，可以通过从 X 中去除单个紧凑的可收缩子流形（或软木塞），然后通过以下幂重新粘合它来获得与给定一个 X 同胚的平滑、闭合、简单连接的 4-流形的任何有限列表边界微分同胚。此外，通过允许软木塞是非紧实的，可以通过这种方式获得所有与 X 同胚的光滑流形的集合。还确定了通用非致密软木塞的存在。