Comparing Bennequin-type inequalities

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 Ozsváth-Szabó $\tau$ 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.

arXiv comment18 pages, 12 figures

References in corpus (7)

• Knot Floer homology and the four-ball genus
• Legendrian knots, transverse knots and combinatorial Floer homology
• Bounds for the Thurston-Bennequin number from Floer homology
• The algebraic crossing number and the braid index of knots and links
• Embedded annuli and Jones' conjecture
• Transverse invariants and right-veering
• The link concordance invariant from Lee homology