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math.GT1998
The Computational Complexity of Knot and Link Problems
Joel Hass, Jeffrey C. Lagarias, Nicholas Pippenger
We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that…
math.GT1998
The number of Reidemeister Moves Needed for Unknotting
Joel Hass, Jeffrey C. Lagarias
There is a positive constant such that for any diagram representing the unknot, there is a sequence of at most Reidemeister moves that will convert it to a tr…
math.GT1998
Simple Closed Geodesics in Hyperbolic 3-Manifolds
Colin Adams, Joel Hass, Peter Scott
This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only ex…