Gromov Invariants and Symplectic Maps
| dc.creator | Ionel, Eleny-Nicoleta | |
| dc.creator | Parker, Thomas H. | |
| dc.date | 1997-03-20 | |
| dc.date.accessioned | 2026-07-07T09:13:01Z | |
| dc.date.available | 2026-07-07T09:13:01Z | |
| dc.description | Given a symplectomorphism f of a symplectic manifold X, one can form the `symplectic mapping cylinder' $X_f = (X \times R \times S^1)/Z$ where the Z action is generated by $(x,s,t)\mapsto (f(x),s+1,t)$. In this paper we compute the Gromov invariants of the manifolds $X_f$ and of fiber sums of the $X_f$ with other symplectic manifolds. This is done by expressing the Gromov invariants in terms of the Lefschetz zeta function of f and, in special cases, in terms of the Alexander polynomials of knots. The result is a large set of interesting non-Kahler symplectic manifolds with computational ways of distinguishing them. In particular, this gives a simple symplectic construction of the `exotic' elliptic surfaces recently discovered by Fintushel and Stern and of related `exotic' symplectic 6-manifolds. | |
| dc.description | 27 pages, AMS-LATEX, 2 figures | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9703013 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9703013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152223 | |
| dc.subject | Differential Geometry | |
| dc.title | Gromov Invariants and Symplectic Maps | |
| dc.type | text |