We consider embeddings of 3-manifolds [Formula: see text] in [Formula: see text] such that the two complementary regions [Formula: see text] and [Formula: see text] each have nilpotent fundamental group. If [Formula: see text] is odd then these groups are abelian and [Formula: see text]. In general [Formula: see text] and [Formula: see text] have 3-generator presentations, and [Formula: see text]. We give two examples illustrating our results.

中文翻译：

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S4 中具有幂等嵌入的 3 流形

我们考虑在 [Formula: see text] 中嵌入 3-manifolds [Formula: see text] 使得两个互补区域 [Formula: see text] 和 [Formula: see text] 每个都具有幂零基团。如果 [Formula: see text] 是奇数，那么这些群是 abelian 和 [Formula: see text]。一般来说[公式：见正文]和[公式：见正文]有3个生成器表示，[公式：见正文]。我们给出了两个例子来说明我们的结果。