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arXiv · 2312.14752

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

Habib Alizadeh·Marcelo S. Atallah·Dylan Cant
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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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Habib Alizadeh, Marcelo S. Atallah, Dylan Cant. 2023-12-22. Lagrangian Intersections and the spectral norm in convex-at-infinity symplectic manifolds. https://arxiv.org/abs/2312.14752

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