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Lagrangian Intersections and the spectral norm in convex-at-infinity symplectic manifolds
- Publication Year :
- 2023
-
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 $L$.<br />Comment: 45 pages
- Subjects :
- Mathematics - Symplectic Geometry
53D35, 53D40, 57R17
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.14752
- Document Type :
- Working Paper