The Computational Complexity of Knot Genus and Spanning Area
Geometric Topology
2007-05-23 v2 Differential Geometry
Abstract
We investigate the computational complexity of some problems in three-dimensional topology and geometry. We show that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. Using similar ideas, we show that deciding whether a curve in a metrized PL 3-manifold bounds a surface of area less than a given constant C is NP-hard.
Keywords
Cite
@article{arxiv.math/0205057,
title = {The Computational Complexity of Knot Genus and Spanning Area},
author = {Ian Agol and Joel Hass and William P. Thurston},
journal= {arXiv preprint arXiv:math/0205057},
year = {2007}
}
Comments
This is a revised version of the previous posting, with many minor clarifications and improvements. 29 pages, 5 figures. To appear in Transactions of the AMS