Displaceability of Certain Constant Sectional Curvature Lagrangian Submanifolds


ŞİRİKÇİ N. İ.

RESULTS IN MATHEMATICS, vol.75, no.4, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 75 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1007/s00025-020-01279-0
  • Journal Name: RESULTS IN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, MathSciNet, zbMATH
  • Keywords: Lagrangian submanifolds, Maslov index, Morse index, Conley-Zehnder index, Primary 53D12, SYMPLECTIC ENERGY, TORIC FIBERS, FLOER THEORY, INTERSECTIONS, INDEX

Abstract

We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain assumptions on the Lagrangian submanifold and on the ambient symplectically aspherical symplectic manifold. The proof utilizes an index relation relating the Maslov index, the Morse index and the Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function, a result on this orbit's Conley-Zehnder index and another result on the Morse indices for constant sectional curvature manifolds the utilization of which to prove nondisplaceability is new.