Add to ORKGGiven a tame knot K presented in the form of a knot diagram, we show that the problem of determining whether K is knotted is in the complexity class NP, assuming the generalized Riemann hypothesis (GRH). In other words, there exists a polynomial-length certificate that can be verified in polynomial time to prove that K is non-trivial. GRH is not needed to believe the certificate, but only to find a short certificate. This result complements the result of Hass, Lagarias, and Pippenger that unknottedness is in NP. Our proof is a corollary of major results of others in algebraic geometry and geometric topology
15 pages, 6 eps-figures, LaTeX-RevTeX4We prove the fractal crumpled structure of collapsed unknotted...
SIGLEAvailable from TIB Hannover: RN 4052(91696-OR) / FIZ - Fachinformationszzentrum Karlsruhe / TIB...
We explore the application of automated reasoning techniques to unknot detection, a classical proble...
Given a tame knot K presented in the form of a knot diagram, we show that the problem of de...
We show that the problem of recognizing that a knot diagram represents a specific torus knot, or any...
We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unk...
We consider the problem of deciding whether a polygonal knot in 3dimensional Euclidean space is unkn...
We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manif...
Knot theory, as traditionally studied, asks whether or not a loop of string is knotted. That is, ca...
Let M n be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-...
The classical knot recognition problem is the problem of determining whether the virtual knot repres...
We investigate the computational complexity of some problems in three-dimensional topology ...
The goal of this paper is to discuss the possibility of finding an algorithm that can give all disti...
A number of results in Hamiltonian graph theory are of the form $\mathcal{P}$$_{1}$ implies $\mathca...
In this thesis we study the computational aspects of knots and knot trans- formations. Most of the p...
15 pages, 6 eps-figures, LaTeX-RevTeX4We prove the fractal crumpled structure of collapsed unknotted...
SIGLEAvailable from TIB Hannover: RN 4052(91696-OR) / FIZ - Fachinformationszzentrum Karlsruhe / TIB...
We explore the application of automated reasoning techniques to unknot detection, a classical proble...
Given a tame knot K presented in the form of a knot diagram, we show that the problem of de...
We show that the problem of recognizing that a knot diagram represents a specific torus knot, or any...
We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unk...
We consider the problem of deciding whether a polygonal knot in 3dimensional Euclidean space is unkn...
We show that the problem of deciding whether a knot in a fixed closed orientable 3-dimensional manif...
Knot theory, as traditionally studied, asks whether or not a loop of string is knotted. That is, ca...
Let M n be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-...
The classical knot recognition problem is the problem of determining whether the virtual knot repres...
We investigate the computational complexity of some problems in three-dimensional topology ...
The goal of this paper is to discuss the possibility of finding an algorithm that can give all disti...
A number of results in Hamiltonian graph theory are of the form $\mathcal{P}$$_{1}$ implies $\mathca...
In this thesis we study the computational aspects of knots and knot trans- formations. Most of the p...
15 pages, 6 eps-figures, LaTeX-RevTeX4We prove the fractal crumpled structure of collapsed unknotted...
SIGLEAvailable from TIB Hannover: RN 4052(91696-OR) / FIZ - Fachinformationszzentrum Karlsruhe / TIB...
We explore the application of automated reasoning techniques to unknot detection, a classical proble...
