Fox再嵌入与Bing子流形
Fox reimbedding and Bing submanifolds
摘要：
设M是可定向的闭连通3-流形。本文引入了M关于闭分离2-流形F的融合Heegaard亏格的概念，并利用它证明了以下两个命题是等价的：（i）紧致连通3-流形Y可以嵌入M，使得Y的象的外部是一个闭体的并;（ii）紧连通3-流形Y可以嵌入到M中，使得M中的每个纽结都可以合点到Y的像内.我们的结果可以看作是Fox [Fox 48]的再嵌入定理和Bing [Bin 58]的3-球面的刻画以及Hass和Thompson [HT 89]和Kobayashi和Nishi [KN 94]的较新结果的一般推广。
英文摘要：
Let M be an orientable closed connected 3-manifold. We introduce the notion of amalgamated Heegaard genus of M with respect to a closed separating 2-manifold F, and use it to show that the following two statements are equivalent: (i) a compact connected 3-manifold Y can be embedded in M so that the exterior of the image of Y is a union of handlebodies; and (ii) a compact connected 3-manifold Y can be embedded in M so that every knot in M can be isotoped to lie within the image of Y . Our result can be regarded as a common generalization of the reimbedding theorem by Fox [Fox48] and the characterization of 3-sphere by Bing [Bin58], as well as more recent results of Hass and Thompson [HT89] and Kobayashi and Nishi [KN94].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
