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# 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} }

- Published 2011 in Symposium on Computational Geometry
DOI:10.1145/1998196.1998218

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 aâ€¦Â CONTINUE READING