Algorithmic unsolvability of the triviality problem for multidimensional knots

Abstract

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

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Keywords

  • Fundamental Group
  • Word Problem
  • Turing Machine
  • Normal Closure
  • Homology Sphere