A central problem in symplectic topology is to understand the topology of exact Lagrangian submanifolds, for instance their ambient homology classes. Using recent developments in Floer homotopy theory, one can now give constraints on their generalised homology or bordism classes, by lifting certain computations from Floer chain complexes to Floer flow categories. This has applications to Arnold’s `nearby Lagrangian submanifold’ conjecture. This talk reports on joint work with Noah Porcelli.
