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arXiv · 2607.25772

Contact Surgery Numbers of the 3-torus

Prerak Deep·Monika Yadav
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Abstract

We study contact surgery numbers for contact structures on the 3-torus. We show that all contact structures obtained via contact surgery along a Legendrian Borromean ring are overtwisted, and that this construction yields infinitely many pairwise non-contactomorphic contact structures on $\mathbb{T}^3$. We prove an obstruction on the maximal Thurston-Bennequin invariant of 3-component links to produce $\mathbb{T}^3$ by Dehn surgery. On a side note, using Legendrian surgery and the ruling invariant, we show that the total symplectic homology of Stein fillings of $(\mathbb{T}^3, \xi_1)$ is non-zero.

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Prerak Deep, Monika Yadav. 2026-07-28. Contact Surgery Numbers of the 3-torus. https://arxiv.org/abs/2607.25772

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