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Floor-crossing for Legendrian Clasp Move
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 Λk of dimension at least two. Moreover, we construct an infinite family of Legendrians 𝒯(Λ,k) from any horizontally displaceable Legendrian Λ in P×ℝ, such that the Chekanov-Eliashberg algebra of 𝒯(Λ,k) admits an augmentation, while 𝒯(Λ,k) has no exact embedded Lagrangian filling of vanishing Maslov class in the symplectization of P× ℝ for sufficiently large k.
Related
- New Heegaard Floer slice genus and clasp number bounds
- Legendrian Reidemeister moves for the convex surface projection
- Bounds on Legendrian Double Twist Knots
- Uniqueness of tangent cones with immersed special Legendrian links
- Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary
BibTeX
@misc{strakos2026floorcrossing,
title = {{Floor-crossing for Legendrian Clasp Move}},
author = {Filip Strakoš},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01381},
eprint = {2609.01381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01381},
}
RIS
TY - UNPB
TI - Floor-crossing for Legendrian Clasp Move
AU - Filip Strakoš
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01381
UR - https://arxiv.org/abs/2609.01381
AB - 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 Λ_k of dimension at least two. Moreover, we construct an infinite family of Legendrians 𝒯(Λ,k) from any horizontally displaceable Legendrian Λ in P×ℝ, such that the Chekanov-Eliashberg algebra of 𝒯(Λ,k) admits an augmentation, while 𝒯(Λ,k) has no exact embedded Lagrangian filling of vanishing Maslov class in the symplectization of P× ℝ for sufficiently large k.
ER -