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arXiv · 1402.2028

A kernel of a braid group representation yields a knot with trivial knot polynomials

Tetsuya Ito
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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.

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Tetsuya Ito. 2014-02-10. A kernel of a braid group representation yields a knot with trivial knot polynomials. https://doi.org/10.1007/s00209-015-1426-7

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