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Problem Does there exist a smooth/PL embedding of 
in 
such that the fundamental group of the complement has an unsolvable word problem?
in such that the fundamental group of the complement has an unsolvable word problem? It's known that there are smooth 
-dimensional submanifolds of whose fundamental groups have unsolvable word problems. The complements of classical knots (
) are known to have solvable word problems, as do arbitrary 
-manifold groups.
Bibliography
A. Dranisnikov, D. Repovs, "Embeddings up to homotopy type in Euclidean Space" Bull. Austral. Math. Soc (1993).
* indicates original appearance(s) of problem.
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