Immersed Lagrangian Floer cohomology via pearly trajectories

[摘要] We define Lagrangian Floer cohomology over Z(2)-coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy a 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 C-n is no less than the sum of its Betti numbers. (C) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-11-01

[关键词] Immersed Lagrangian;Floer cohomology;Positivity;Pearly trajectory