2006/06/23 by Albers, Peter
#53D12 #53D40 #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.math/0606600
In general, Lagrangian Floer homology - if well-defined - is not isomorphic to singular homology. For arbitrary closed Lagrangian submanifolds a local version of Floer homology is defined in [Flo89, Oh96] which is isomorphic to singular homology. This construction assumes that the involved Hamiltonian function H is sufficiently C2-small and the almost complex structure is sufficiently standard. In this note we develop a new construction of local Floer homology which works for any (compatible) almost complex structure and all Hamiltonian function with Hofer norm less than the minimal (symplectic) area of a holomorphic disk or sphere. The example S1⊂\C shows that this is sharp. If the Lagrangian submanifold is monotone, the grading of local Floer homology can be improved to a \Z-grading.