Uniform thickness criterion for fibered knots

Let KS3K\subset S^3 be a fibered knot, and let ξK\xi_K be the contact structure induced by an open-book decomposition of KK. Let ξStd\xi_{Std} denote the standard contact structure on S3S^3. Uniform thickness criterion. The knot KK is uniformly thick if and only if

ξKξStd.\xi_K\neq\xi_{Std}.

This proposed characterization connects uniform thickness with the contact structure supported by a fibered knot. The source explicitly says that the other direction remains an interesting open question, so the equivalence is not established.

Sources & referencesView supporting material

Primary source

Andrew McCullough, “Legendrian Large Cables And New Phenomenon For Non-Uniformly Thick Knots”, arXiv:1810.12327 (2020).

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