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The Defect of the Bennequin-Eliashberg Inequality and Bennequin Surfaces
Journal article   Peer reviewed

The Defect of the Bennequin-Eliashberg Inequality and Bennequin Surfaces

Tetsuya Ito and Keiko Kawamuro
Indiana University mathematics journal, Vol.68(3), pp.799-833
01/01/2019
DOI: 10.1512/iumj.2019.68.7662

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Abstract

For a null-homologous transverse link T in a general contact manifold with an open book, we explore strongly quasipositive braids and Bennequin surfaces. We define the defect delta (T) of the Bennequin-Eliashberg inequality. We study relations between delta (T) and minimal genus Bennequin surfaces of T. In particular, in the disk open book case, under some large fractional Dehn twist coefficient assumption, we show that delta (T) = N if and only if 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.
Mathematics Physical Sciences Science & Technology

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