Dylan Cant

English · Français · 中文

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

Habib Alizadeh、Marcelo S. Atallah、Dylan Cant

2023年12月。发表于 Math. Z. 310 (2025), Paper No. 2

摘要：

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 $L$.

链接：

• PDF
• arXiv:2312.14752
• 期刊版本（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},
  }