# Unsolvability of word problem for 2-knot complements

**Problem**Does there exist a smooth/PL embedding of 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.