Arnol'd's Lagrangian intersection conjecture
Arnol'd's Lagrangian intersection conjecture
Let be a closed smooth manifold and let denote its cotangent bundle. For every compactly supported Hamiltonian diffeomorphism of , consider the intersection points of the zero section with its image . Arnol'd's conjecture. The number of intersection points is bounded from below by the minimal number of critical points of a smooth function on . This is the Lagrangian version of Arnol'd's conjecture for cotangent bundles and motivates lower bounds for Lagrangian intersections; the source does not provide enough information here to determine whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Habib Alizadeh, Marcelo S. Atallah and Dylan Cant, “Lagrangian Intersections and the spectral norm in convex-at-infinity symplectic manifolds”, arXiv:2312.14752 (2023).
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