Symplectic symmetries of 4-manifolds
| dc.creator | Chen, Weimin | |
| dc.creator | Kwasik, Slawomir | |
| dc.date | 2007-09-11 | |
| dc.date.accessioned | 2026-07-07T08:28:49Z | |
| dc.date.available | 2026-07-07T08:28:49Z | |
| dc.description | A study of symplectic actions of a finite group $G$ on smooth 4-manifolds is initiated. The central new idea is the use of $G$-equivariant Seiberg-Witten-Taubes theory in studying the structure of the fixed-point set of these symmetries. The main result in this paper is a complete description of the fixed-point set structure (and the action around it) of a symplectic cyclic action of prime order on a minimal symplectic 4-manifold with $c_1^2=0$. Comparison of this result with the case of locally linear topological actions is made. As an application of these considerations, the triviality of many such actions on a large class of 4-manifolds is established. In particular, we show the triviality of homologically trivial symplectic symmetries of a $K3$ surface (in analogy with holomorphic automorphisms). Various examples and comments illustrating our considerations are also included. | |
| dc.description | 28 pages, 1 figure, 1 appendix, published | |
| dc.identifier | https://arxiv.org/abs/0709.1708 | |
| dc.identifier | http://arxiv.org/abs/0709.1708 | |
| dc.identifier | Topology, Vol. 46, No.2 (2007), 103-128 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137755 | |
| dc.subject | Geometric Topology | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 57S15 (Primary); 57R17 (Secondary) | |
| dc.title | Symplectic symmetries of 4-manifolds | |
| dc.type | text |