Mathematics – Symplectic Geometry
Scientific paper
2004-04-06
Mathematics
Symplectic Geometry
14 pages, some typos and errors corrected
Scientific paper
Lalonde and McDuff showed that the natural action of the rational homology of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M, \omega)$ on the rational homology groups $H_*(M,{\mathbb Q})$ is trivial. In this note, given a symplectic action of SU(2), $\phi:SU(2)\times M \to M$, we will construct a symplectic fiber bundle $P_\phi\to {\mathbb CP}^2$ with fiber $(M,\omega)$ 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 $\phi$ and do some explicit calculations.
No associations
LandOfFree
Triviality of symplectic SU(2)-actions on homology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Triviality of symplectic SU(2)-actions on homology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Triviality of symplectic SU(2)-actions on homology will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-601393