Obstructions to the existence of displaceable Lagrangian submanifolds

Lagrangian submanifold;Maslov index;Conley-Zehnder index;Floer theory;Hamiltonian flows

Sirikci, Nil Ipek

关键词: Lagrangian submanifold;    Maslov index;    Conley-Zehnder index;    Floer theory;    Hamiltonian flows;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/32007/Sirikci_NilIpek.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We utilize Floer theory and an index relation relating the Maslov index, Morse index and Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function to state and prove some nonexistence results for certain displaceable Lagrangian submanifolds. We start with results under the assumption that the symplectic manifold (M,w) is closed and symplectically aspherical and then generalize to the case when (M,w) is weakly exact. The specific Lagrangian submanifolds in consideration are split hyperbolic submanifolds, spheres, products of spheres, Cayley projective plane and quaternionic projective spaces.