Binding Numbers of Tight Contact Structures on $L(n,1)$

Csaba Daniel Farkas

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arXiv · 2607.21229

Binding Numbers of Tight Contact Structures on $L(n,1)$

Csaba Daniel Farkas

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Abstract

We study binding numbers of tight contact structures on the lens spaces $L(n,1)$. Using the $d_3-$invariant, together with restrictions on planar monodromy factorizations and the Durst-Kegel algorithm for computing $d_3$ from open books, we obtain lower bounds for the number of binding components of planar open books supporting these contact structures. As a consequence, we compute the binding number of the universally tight contact structures on $L(n,1)$, showing that it is equal to $n$.

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Csaba Daniel Farkas. 2026-07-23. Binding Numbers of Tight Contact Structures on $L(n,1)$. https://arxiv.org/abs/2607.21229

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