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Legendrian graphs and quasipositive diagrams. (English) Zbl 1206.57005

A link is called quasipositive if it has a diagram which is the closure of a product of conjugates of the positive generators of the braid group. The authors clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, they give an alternative proof of the following result by M. Hedden [J. Knot Theory Ramifications 19, No. 5, 617–629 (2010; Zbl 1195.57029)]. Let \(F\) be a fiber surface in \(S^3\). \(F\) is quasipositive if and only if \(F\) is compatible with the standard contact structure on \(S^3\).

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
53D10 Contact manifolds (general theory)
57R17 Symplectic and contact topology in high or arbitrary dimension

Citations:

Zbl 1195.57029
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References:

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