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arXiv · 2507.16747

Exact Lagrangian fillability of 3-braid closures

James Hughes·Jiajie Ma
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Abstract

We determine when a Legendrian quasipositive 3-braid closure in standard contact $\mathbb{R}^3$ admits an orientable or non-orientable exact Lagrangian filling. Our main result provides evidence for the orientable fillability conjecture of Hayden and Sabloff, showing that a 3-braid closure is orientably exact Lagrangian fillable if and only if it is quasipositive and the HOMFLY bound on its maximum Thurston-Bennequin number is sharp. Of possible independent interest, we construct explicit Legendrian representatives of quasipositive 3-braid closures with maximum Thurston-Bennequin number.

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James Hughes, Jiajie Ma. 2025-07-22. Exact Lagrangian fillability of 3-braid closures. https://arxiv.org/abs/2507.16747

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