Triviality of symplectic SU(2)-actions on homology
| dc.creator | Ozan, Yildiray | |
| dc.date | 2004-04-06 | |
| dc.date | 2006-05-20 | |
| dc.date.accessioned | 2026-07-07T06:36:41Z | |
| dc.date.available | 2026-07-07T06:36:41Z | |
| dc.description | Lalonde and McDuff showed that the natural action of the rational homology of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M, ω)$ on the rational homology groups $H_*(M,{\mathbb Q})$ is trivial. In this note, given a symplectic action of SU(2), $ϕ:SU(2)\times M \to M$, we will construct a symplectic fiber bundle $P_ϕ\to {\mathbb CP}^2$ with fiber $(M,ω)$ and use it to construct the chains, which bound the images of the homology cycles under the trace map given by the SU(2)-action. It turns out that the natural chains bounded by the SU(2)-orbits in $M$ are punctured ${\mathbb CP}^2$'s, the counter parts of holomorphic discs bounding circles in case of Hamiltonian circle actions. We will also define some invariants of the action $ϕ$ and do some explicit calculations. | |
| dc.description | 14 pages, some typos and errors corrected | |
| dc.identifier | https://arxiv.org/abs/math/0404121 | |
| dc.identifier | http://arxiv.org/abs/math/0404121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100162 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D20; 14P25 | |
| dc.title | Triviality of symplectic SU(2)-actions on homology | |
| dc.type | text |