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Free, publicly-accessible full text available December 1, 2025
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In this paper, we observe that the hat version of the Heegaard Floer invariant of Legendrian knots in contact three-manifolds defined by Lisca-Ozsváth-Stipsicz-Szabó can be combinatorially computed. We rely on Plamenevskaya’s combinatorial description of the Heegaard Floer contact invariant.more » « less
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Wood, David R.; de Gier, Jan; Praeger, Cheryl E.; Tao, Terence (Ed.)Using the 10/8 + 4 theorem of Hopkins, Lin, Shi, and Xu, we derive a smooth slicing obstruction for knots in the three-sphere using a spin 4-manifold whose boundary is 0–surgery on a knot. This improves upon the slicing obstruction bound by Vafaee and Donald that relies on Furuta’s 10/8 theorem. We give an example where our obstruction is able to detect the smooth non-sliceness of a knot by using a spin 4-manifold for which the Donald-Vafaee slice obstruction fails.more » « less
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null (Ed.)The slice-Bennequin inequality gives 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.more » « less
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Acu, Bahar; Cannizzo, Catherine; McDuff, Dusa; Myer, Ziva; Pan, Yu; Traynor, Lisa (Ed.)
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