Dylan Cant

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Lagrangian intersections and the spectral norm in convex-at-infinity symplectic manifolds

Habib Alizadeh, Marcelo S. Atallah, Dylan Cant

12-2023. Published in Math. Z. 310 (2025), Paper No. 2

Abstract:

Given a compact Lagrangian $L$ in a semipositive convex-at-infinity symplectic manifold $W$, we establish a cup-length estimate for the action values of $L$ associated to a Hamiltonian isotopy whose spectral norm is smaller than some $\hbar(L)$. When $L$ is rational, this implies a cup-length estimate on the number of intersection points. This Chekanov-type result generalizes a theorem of Kislev and Shelukhin proving non-displaceability in the case when $W$ is closed and monotone. The method of proof is to deform the pair-of-pants product on Hamiltonian Floer cohomology using the Lagrangian $L$.

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• arXiv:2312.14752
• Published version (Math. Z.)
• BibTeX

  @article{cup-length,
    author        = {Habib Alizadeh and Marcelo S. Atallah and Dylan Cant},
    title         = {Lagrangian intersections and the spectral norm in convex-at-infinity symplectic manifolds},
    journal       = {Math. Z.},
    year          = {2025},
    volume        = {310},
    number        = {1},
    pages         = {Paper No. 2},
    doi           = {10.1007/s00209-025-03710-0},
    eprint        = {2312.14752},
    archivePrefix = {arXiv},
    primaryClass  = {math.SG},
  }