Does the Jones polynomial detect the unknot?

Details Does the Jones polynomial detect the unknot? Does the Jones polynomial detect the unknot?

2000-12-12

arxiv.org/abs/math/0012086v1

Mathematics

Geometric Topology

12 pages, 3 figures

Scientific paper

We address the question: Does there exist a non-trivial knot with a trivial
Jones polynomial? To find such a knot, it is almost certainly sufficient to
find a non-trivial braid on four strands in the kernel of the Burau
representation. I will describe a computer algorithm to search for such a
braid.

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