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

作者：Ito Tetsuya^*

来源：Mathematische Zeitschrift, 2015, 280(1-2): 347-353.

DOI：10.1007/s00209-015-1426-7

• Knots
• Dehornoy ordering
• Quantum invariants

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 the 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.

• 出版日期2015-6