The least spanning area of a knot and the optimal bounding chain problem

@inproceedings{Dunfield2011TheLS,
  title={The least spanning area of a knot and the optimal bounding chain problem},
  author={Nathan M. Dunfield and Anil N. Hirani},
  booktitle={Symposium on Computational Geometry},
  year={2011}
}
Two fundamental objects in knot theory are the minimal genus surface and the least area surface bounded by a knot in a 3-dimensional manifold. When the knot is embedded in a general 3-manifold, the problems of finding these surfaces were shown to be NP-complete and NP-hard respectively. However, there is evidence that the special case when the ambient manifold is R^3, or more generally when the second homology is trivial, should be considerably more tractable. Indeed, we show here that a… CONTINUE READING