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A classification of smooth embeddings of 3-manifolds in 6-space. (English) Zbl 1167.57013
The paper studies the classical Knotting Problem in differential topology, namely for a given smooth \(n\)-manifold \(N\) and a given number \(m\) to describe the isotopy classes of embeddings \(N\to{\mathbb R}^m\). There is a vast literature on this problem and adequate references are given. Among the remaining open problems, the author addresses specifically the case \((m, n) = (6, 3)\) for \(N\) a closed connected orientable 3-manifold, and, more generally, \(2m = 3n + 3\).
The main result is a description of the set \(\text{Emb}^6(N)\) of embeddings of the 3-manifold \(N\) into \({\mathbb R}^6\) up to isotopy. The description is given in terms of invariants due to Whitney and Kreck, the definitions of which are properly recalled in the paper.

MSC:
57R40 Embeddings in differential topology
57R52 Isotopy in differential topology
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