We prove that for any fixedn≥3 there is no algorithm deciding whether or not a given knotf: S n→ℝn+2 is trivial. Some related results, are also presented.
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Both authors were partially supported by NSF grants.
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Nabutovsky, A., Weinberger, S. Algorithmic unsolvability of the triviality problem for multidimensional knots. Commentarii Mathematici Helvetici 71, 426–434 (1996). https://doi.org/10.1007/BF02566428
- Fundamental Group
- Word Problem
- Turing Machine
- Normal Closure
- Homology Sphere