2007/01/31 by Kenji Fukaya, Paul Seidel, Ivan Smith · 43 citations
Mathematics · #Class (philosophy) #Cotangent bundle #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Inverse problem for Lagrangian mechanics #Lagrangian #Trigonometric functions #math.SG #msc:53D35 #msc:53D40
paper · pdf · doi:10.1007/s00222-007-0092-8
published in Inventiones mathematicae 172(1), 1-27 (Springer Science+Business Media) · 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor changes
arxiv created 2007/09/13 · openalex publication_date 2007/12/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.