A note on local Floer homology
| dc.creator | Albers, Peter | |
| dc.date | 2006-06-23 | |
| dc.date.accessioned | 2026-07-07T07:17:38Z | |
| dc.date.available | 2026-07-07T07:17:38Z | |
| dc.description | 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 $C^2$-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 $S^1\subset\C$ shows that this is sharp. If the Lagrangian submanifold is monotone, the grading of local Floer homology can be improved to a $\Z$-grading. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606600 | |
| dc.identifier | http://arxiv.org/abs/math/0606600 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114007 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D40, 53D12 | |
| dc.title | A note on local Floer homology | |
| dc.type | text |