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A remarkable 20-crossing tangle

Abstract

For any positive integer r, we exhibit a knot Kr with (20 · 2 r−1 + 1) crossings whose Jones polynomial V (Kr) is equal to 1 mod-ulo 2 r. Our construction rests on a certain 20-crossing tangle T 20 which is undetectable by the Kauffman bracket polynomial pair mod 2.
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Dates and versions

hal-01382778 , version 1 (17-10-2016)
hal-01382778 , version 2 (16-01-2017)

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Shalom Eliahou, Jean Fromentin. A remarkable 20-crossing tangle. 2016. ⟨hal-01382778v2⟩
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