1988/09/01 by Andreas Floer · 333 citations
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematics #Symplectic geometry #Action (physics) #Symplectic manifold #Pure mathematics #Transversality #Flow (mathematics) #Bounded function #Compact space #Manifold (fluid mechanics) #Space (punctuation) #Mathematical analysis #Geometry
paper · doi:10.1002/cpa.3160410603
published in Communications on Pure and Applied Mathematics 41(6), 775-813 (Wiley)
openalex publication_date 1988/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Abstract The symplectic action can be defined on the space of smooth paths in a symplectic manifold P which join two Lagrangian submanifolds of P . To pursue a new approach to the variational theory of this function, we define on a subset of the path space the flow whose trajectories are given by the solutions of the Cauchy‐Riemann equation with respect to a suitable almost complex structure on P . In particular, we prove compactness and transversality results for the set of bounded trajectories.