On the finiteness of higher knot sums

@article{Dunwoody1987OnTF,
  title={On the finiteness of higher knot sums},
  author={M. J. Dunwoody and R. Fenn},
  journal={Topology},
  year={1987},
  volume={26},
  pages={337-343}
}
Abstract In this paper we show that any higher knot ( n ≥3) can be decomposed as a sum of irreducible knots and there is a finite upper bound on the number of summands. The case n =1 is due to Schubert [10]. A proof of this present case was published in [12] by Soninskii but subsequently Maeda showed that a crucial lemma was false [7]. The difficulty is to find a bound on decompositions of the knot group π 1 . This is achieved here by applying Dunwoody's work in [3]. This results in two… Expand
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