University of Toronto's Symplectic Geometry Seminar

Abstract: Let L and L' be Lagrangian submanifolds of a closed symplectic manifold. When L' is a C^1 small Hamiltonian deformation of L, Chekanov and Oh observed that the associated Floer complex undergoes a thick and thin decomposition. As L' deforms further, Chekanov observed that some algebraic information is retained. We use this information ('\lambda homotopy') to show that certain cap moduli spaces in Lagrangian Floer homology are not empty and as an application prove that the Hamiltonian group is flat under the Hofer and spectral norms.