Algebraic overtwistedness of contact (+1)-surgeries via augmented Floer theories

Abstract

We prove that contact (+1)-surgery along a Legendrian n-sphere Λ⊂(𝕊²ⁿ⁺¹,ξ_std) with tb(Λ)≠ (−1)^{(n(n−1))/2+1} has vanishing contact homology. In dimension three, this produces new examples of tight algebraically overtwisted contact manifolds, vastly extending the authors' previous results: If a Legendrian knot in (𝕊³,ξ_std) admits an exact, oriented Lagrangian filling that is not a disk, then contact (+1/k)-surgery on it is algebraically overtwisted and tight for every positive integer k. Our proofs use versions of symplectic cohomology and wrapped Floer cohomology defined by augmentations of a chain-level contact homology algebra.

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BibTeX

@misc{avdek2026algebraic,
  title = {{Algebraic overtwistedness of contact $(+1)$-surgeries via augmented Floer theories}},
  author = {Russell Avdek and Youlin Li and Zhengyi Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19333},
  eprint = {2610.19333},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19333},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Algebraic overtwistedness of contact (+1)-surgeries via augmented Floer theories
AU  - Russell Avdek
AU  - Youlin Li
AU  - Zhengyi Zhou
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19333
UR  - https://arxiv.org/abs/2610.19333
AB  - We prove that contact (+1)-surgery along a Legendrian n-sphere Λ⊂(𝕊^2n+1,ξ_std) with tb(Λ)≠ (−1)^(n(n−1))/2+1 has vanishing contact homology. In dimension three, this produces new examples of tight algebraically overtwisted contact manifolds, vastly extending the authors' previous results: If a Legendrian knot in (𝕊^3,ξ_std) admits an exact, oriented Lagrangian filling that is not a disk, then contact (+1/k)-surgery on it is algebraically overtwisted and tight for every positive integer k. Our proofs use versions of symplectic cohomology and wrapped Floer cohomology defined by augmentations of a chain-level contact homology algebra.
ER  -

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