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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
##### Keywords:
embedding; isotopy; smoothing; 3-manifolds; surgery
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##### References:
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