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arXiv · 2609.01381

Floor-crossing for Legendrian Clasp Move

Filip Strakoš
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Abstract

We investigate the effect of the clasp move of Legendrian submanifolds of dimension at least two on the moduli spaces of pseudo-holomorphic curves that contribute to the differential of the Chekanov-Eliashberg algebra. As an application, we compute the differential of Chekanov-Eliashberg algebra of twist spheres $\Lambda_k$ of dimension at least two. Moreover, we construct an infinite family of Legendrians $\mathcal{T}(\Lambda,k)$ from any horizontally displaceable Legendrian $\Lambda$ in $P\times\mathbb{R}$, such that the Chekanov-Eliashberg algebra of $\mathcal{T}(\Lambda,k)$ admits an augmentation, while $\mathcal{T}(\Lambda,k)$ has no exact embedded Lagrangian filling of vanishing Maslov class in the symplectization of $P\times \mathbb{R}$ for sufficiently large $k$.

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Filip Strakoš. 2026-09-01. Floor-crossing for Legendrian Clasp Move. https://arxiv.org/abs/2609.01381

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