Computing closed essential surfaces in knot complements

@inproceedings{Burton2012ComputingCE,
  title={Computing closed essential surfaces in knot complements},
  author={Benjamin A. Burton and Alexander Coward and Stephan Tillmann},
  booktitle={International Symposium on Computational Geometry},
  year={2012}
}
We present a new, practical algorithm to test whether a knot complement contains a closed essential surface. This property has important theoretical and algorithmic consequences. However systematically testing it has until now been infeasibly slow, and current techniques only apply to specific families of knots. As a testament to its practicality, we run the algorithm over a comprehensive body of 2979 knots, including the two 20-crossing dodecahedral knots, yielding results that were not… 

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