A kernel of a braid group representation yields a knot with trivial knot polynomials
Geometric Topology
2017-04-10 v1
Abstract
We show that a non-trivial, non-central normal subgroup of the braid groups contains a braid whose closure is a hyperbolic knot with arbitrary large genus. This shows that non-faithfulness of a quantum representation implies that the corresponding quantum invariant fails to detect the unknot. The proof utilizes the Dehornoy ordering of the braid groups.
Keywords
Cite
@article{arxiv.1402.2028,
title = {A kernel of a braid group representation yields a knot with trivial knot polynomials},
author = {Tetsuya Ito},
journal= {arXiv preprint arXiv:1402.2028},
year = {2017}
}