2017/03/27 by Tetsuya Ito, Ito, Tetsuya, Keiko Kawamuro +1 · 1 citation
Mathematics · Medicine · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Bone health and treatments
paper · pdf · doi:10.48550/arxiv.1703.09322
For a null-homologous transverse link \mathcal T in a general contact manifold with an open book, we explore strongly quasipositive braids and Bennequin surfaces. We define the defect δ(\mathcal T) of the Bennequin-Eliashberg inequality. We study relations between δ(\mathcal T) and minimal genus Bennequin surfaces of \mathcal T. In particular, in the disk open book case, under some large fractional Dehn twist coefficient assumption, we show that δ(\mathcal T)=N if and only if \mathcal T is the boundary of a Bennequin surface with exactly N negatively twisted bands. That is, the Bennequin inequality is sharp if and only if it is the closure of a strongly quasipositive braid.