3-球面的子流形的扭解
Unknotting submanifolds of the 3-sphere by twistings
摘要：
根据Fox重嵌入定理，3-球面的任何紧致子流形都可以重嵌入到3-球面中，从而使其不打结。目前还不清楚福克斯的重新嵌入是否可以用扭曲来取代。在本文中，我们将证明任何嵌入在3-球面中的闭2-流形都可以通过扭曲来解结。尽管有这种现象，我们证明了存在一个紧的3-子流形的3-球，不能unknoted扭曲。这表明，福克斯的重新嵌入并不总是被扭曲所取代。
英文摘要：
By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed 2-manifold embedded in the 3-sphere can be unknotted by twistings. In spite of this phenomenon, we show that there exists a compact 3-submanifold of the 3-sphere which cannot be unknotted by twistings. This shows that the Fox's re-embedding cannot always be replaced with twistings.
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