2020/10/04 by Aceves, Elaina, Kawamuro, Keiko, Truong, Linh
#57K10 #57K18 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2010.01673
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 τ-Bennequin inequalities provide upper bounds on the self-linking number of a knot in terms of the Rasmussen s invariant and the Ozsváth-Szabó τ 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 τ-Bennequin inequality are both sharp.