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Fuchs–Tabachnikov conjecture on transversal knots with fixed knot type and Bennequin number
Fuchs–Tabachnikov conjecture. Two transversal knots of $\mathbb{R}^3$ with the same knot type and the same Bennequin number are contact isotopic.
Conjecturerefutedcontact-topology transversal-knotsarXiv posted 2 days ago

Fuchs–Tabachnikov conjecture on transversal knots with fixed knot type and Bennequin number