2005/12/31 by P. Albers, Peter Albers · 15 citations
Mathematics · #Advanced Combinatorial Mathematics #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Intersection homology #Khovanov homology #Morse homology #Singular homology #Symplectic geometry #math.SG #msc:37J05 #msc:53D12 #msc:53D40 #msc:57R17
paper · pdf · doi:10.1093/imrn/rnm134
published in International Mathematics Research Notices (Oxford University Press) · 41 pages, 14 figures. v2: major revision, v3: included detailed transversality proofs. accepted by IMRN
arxiv created 2007/11/01 · openalex publication_date 2007/12/12 · arxiv updated 2011/11/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This article addresses two issues. First, we explore to what extent the techniques of Piunikhin, Salamon and Schwarz in [18] can be carried over to Lagrangian Floer homology. In [18] an isomorphism between Hamiltonian Floer homology and singular homology is established. In contrast, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian submanifold, in general. Depending on the minimalMaslov number, we construct for certain degrees two homomorphisms between Lagrangian Floer homology and singular homology. In degrees, where both maps are defined, we prove them to be isomorphisms. Examples show that this statement is sharp. Second, we construct two comparison homomorphisms between Lagrangian and Hamiltonian Floer homology. They are defined without degree restrictions and are proven to be the natural analogs to the homomorphisms in singular homology induced by the inclusion map of the Lagrangian submanifold into the ambient symplectic manifold.