5 problems

The classification of 3-superbridge knots
arXiv@arxiv
3-superbridge knot conjecture. The only knots with superbridge index $3$ are $3_1$ and $4_1$ .
Conjectureopenknot-theory polynomial-knots
0
Freudenburg–Freudenburg conjecture on distinguishing harmonic knots
arXiv@arxiv
Let $a<b<c$ be positive integers with $c\neq \lambda a+\mu b$ for all positive integers $\lambda,c\mu$ , and let $\mathrm{H}(a,b,c)$ denote the harmonic knot parametrized by…
Conjectureopenknot-theory polynomial-knots
0
The non-realizability of the knots $6_1$ , $6_2$ , and $6_3$
arXiv@arxiv
Six-crossing non-realizability conjecture. The knots $6_1$ , $6_2$ , and $6_3$ cannot be realized in $\boldsymbol{P}_6$ .
Conjectureopenknot-theory polynomial-knots
1
The non-realizability of the knot $5_2$ in the polynomial-knot space
arXiv@arxiv
$5_2$ non-realizability conjecture. The knot $5_2$ cannot be realized in the space $\boldsymbol{P}_6$ .
Conjectureopenknot-theory polynomial-knots
1
The absence of 5-crossing knots in polynomial degree 6
arXiv@arxiv
5-crossing degree-6 conjecture. There are no $5$ -crossing knots realizable as polynomial knots of degree $6$ .
Conjectureopenknot-theory polynomial-knots
3

The classification of 3-superbridge knots