Comparing Bennequin-type inequalities

Elaina Aceves; Keiko Kawamuro; Linh Truong

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arXiv · 2010.01673

Comparing Bennequin-type inequalities

Elaina Aceves·Keiko Kawamuro·Linh Truong

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Abstract

The slice-Bennequin inequality states an upper bound for the self-linking number of a knot in terms of its four-ball genus. The $s$-Bennequin and $\tau$-Bennequin inequalities provide upper bounds on the self-linking number of a knot in terms of the Rasmussen $s$ invariant and the Ozsv\'ath-Szab\'o $\tau$ invariant. We exhibit examples in which the difference between self-linking number and four-ball genus grows arbitrarily large, whereas the $s$-Bennequin inequality and the $\tau$-Bennequin inequality are both sharp.

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Elaina Aceves, Keiko Kawamuro, Linh Truong. 2020-10-04. Comparing Bennequin-type inequalities. https://arxiv.org/abs/2010.01673

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