Symplectomorphism groups and embeddings of balls into rational ruled 4-manifolds
| dc.creator | Pinsonnault, Martin | |
| dc.date | 2006-03-13 | |
| dc.date | 2009-05-15 | |
| dc.date.accessioned | 2026-07-07T13:15:42Z | |
| dc.date.available | 2026-07-07T13:15:42Z | |
| dc.description | Let $X$ be any rational ruled symplectic four-manifold. Given a symplectic embedding $ι:B_{c}\into X$ of the standard ball of capacity $c$ into $X$, consider the corresponding symplectic blow-up $\tX_ι$. In this paper, we study the homotopy type of the symplectomorphism group $\Symp(\tX_ι)$, simplifying and extending the results of math.SG/0207096. This allows us to compute the rational homotopy groups of the space $\IEmb(B_{c},X)$ of unparametrized symplectic embeddings of $B_{c}$ into $X$. We also show that the embedding space of one ball in $CP^2$, and the embedding space of two disjoint balls in $CP^2$, if non empty, are always homotopy equivalent to the corresponding spaces of ordered configurations. Our method relies on the theory of pseudo-holomorphic curves in 4-manifolds, on the theory of Gromov invariants, and on the inflation technique of Lalonde-McDuff. | |
| dc.description | New title, new abstract, content now agrees with the published version, small correction to the proof of Theorem 1.10. A sequel to the paper SG/0207096 | |
| dc.identifier | https://arxiv.org/abs/math/0603310 | |
| dc.identifier | http://arxiv.org/abs/math/0603310 | |
| dc.identifier | Compositio Math. 144 (2008) 787-810 | |
| dc.identifier | doi:10.1112/S0010437X0700334X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230555 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53D35; 57R17; 55R20; 57S05 | |
| dc.title | Symplectomorphism groups and embeddings of balls into rational ruled 4-manifolds | |
| dc.type | text |