2021/11/30 by Wenmin Gong, Gong, Wenmin · 1 citation
Mathematics · #53D12 #53D40 #57R17 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2111.15442
openalex publication_date 2021/11/30 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28
We prove a degenerate homological Arnol'd conjecture on Lagrangian intersections beyond the case studied by A. Floer and H. Hofer via a new version of Lagrangian Ljusternik--Schnirelman theory. We introduce the notion of (Lagrangian) fundamental quantum factorizations and use them to give some uniform lower bounds of the numbers of Lagrangian intersections for some classical examples including Clifford tori in complex projective spaces. Additionally, we use the Lagrangian Ljusternik-Schnirelman theory to study the size of the intersection of a monotone Lagrangian with its image of a Hamiltonian diffeomorphism.