2019/07/06 by Garrett Alston, Alston, Garrett, Erkao Bao +1
Mathematics · #53D12 #53D40 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1907.03072
openalex publication_date 2019/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define Lagrangian Floer cohomology over \mathbb Z2-coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy certain positivity condition on the index of the non-embedded points, and show that it is an invariant of the Lagrangian immersion under Hamiltonian deformations. We also show that it is naturally isomorphic to the Hamiltonian perturbed version of Lagrangian Floer cohomology as defined in [4]. As an application, we prove that the number of non-embedded points of such a Lagrangian in \mathbb Cn is no less than the sum of its Betti numbers.