An index inequality for embedded pseudoholomorphic curves in symplectizations
| dc.creator | Hutchings, Michael | |
| dc.date | 2001-12-17 | |
| dc.date.accessioned | 2026-07-07T04:45:17Z | |
| dc.date.available | 2026-07-07T04:45:17Z | |
| dc.description | Let $Σ$ be a surface with a symplectic form, let $ϕ$ be a symplectomorphism of $Σ$, and let $Y$ be the mapping torus of $ϕ$. We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in $\R\times Y$, with cylindrical ends asymptotic to periodic orbits of $ϕ$ or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand the Seiberg-Witten Floer homology of $Y$ in terms of such pseudoholomorphic curves. Analogues of our results should also hold in three dimensional contact homology. | |
| dc.description | 60 pages, LaTeX 2e | |
| dc.identifier | https://arxiv.org/abs/math/0112165 | |
| dc.identifier | http://arxiv.org/abs/math/0112165 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62902 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.title | An index inequality for embedded pseudoholomorphic curves in symplectizations | |
| dc.type | text |