Does the Jones polynomial detect the unknot?

Stephen J. Bigelow

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Does the Jones polynomial detect the unknot?

Stephen J. Bigelow

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Abstract

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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BibTeX RIS

Stephen J. Bigelow. 2000-12-12. Does the Jones polynomial detect the unknot?. https://arxiv.org/abs/math/0012086

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