2008/12/01 by Jean-Yves Welschinger, Welschinger, Jean-Yves · 1 citation
Computer Science · Mathematics · #53D40 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.SG #msc:53D40 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0812.0276
44 pages, 9 figures
arxiv created 2008/12/01 · openalex publication_date 2008/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a contravariant functor, called Floer functor, from the category of Lagrangian conductors of a symplectic manifold to the homotopy category of bounded chain complexes of open strings in this manifold. The latter two categories are defined for all symplectic manifolds, whereas Floer functor is defined for semipositive manifolds which are either closed or convex at infinity. We then prove that when the first Chern class of the symplectic manifold vanishes, Lagrangian spheres define Lagrangian conductors so that in particular their integral Floer cohomology is well defined. This requires the introduction of singular almost-complex structures given by symplectic field theory.