Minimality and symplectic sums
| dc.creator | Usher, Michael | |
| dc.date | 2006-06-21 | |
| dc.date | 2007-10-02 | |
| dc.date.accessioned | 2026-07-07T08:33:23Z | |
| dc.date.available | 2026-07-07T08:33:23Z | |
| dc.description | Let X_1, X_2 be symplectic 4-manifolds containing symplectic surfaces F_1,F_2 of identical positive genus and opposite squares. Let Z denote the symplectic sum of X_1 and X_2 along the F_k. Using relative Gromov--Witten theory, we determine precisely when the symplectic 4-manifold Z is minimal (i.e., cannot be blown down); in particular, we prove that Z is minimal unless either: one of the X_k contains a (-1)-sphere disjoint from F_k; or one of the X_k admits a ruling with F_k as a section. As special cases, this proves a conjecture of Stipsicz asserting the minimality of fiber sums of Lefschetz fibrations, and implies that the non-spin examples constructed by Gompf in his study of the geography problem are minimal. | |
| dc.description | The numbering has been brought into agreement with that in the published version. No change in content. 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606543 | |
| dc.identifier | http://arxiv.org/abs/math/0606543 | |
| dc.identifier | Internat. Math. Res. Not. 2006, Article ID 49857 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139109 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R17 | |
| dc.title | Minimality and symplectic sums | |
| dc.type | text |