Families of Simply Connected 4-Manifolds with the Same Seiberg-Witten Invariants
| dc.creator | Fintushel, Ronald | |
| dc.creator | Stern, Ronald J. | |
| dc.date | 2002-10-14 | |
| dc.date.accessioned | 2026-07-07T04:51:55Z | |
| dc.date.available | 2026-07-07T04:51:55Z | |
| dc.description | This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their construction, seem to be quite different, but cannot be distinguished by Seiberg-Witten invariants. Whether these manifolds are, or are not, actually diffeomorphic seems to be a very difficult question to answer. The most interesting of these constructions is a surgery that from certain symplectic 4-manifolds will produce nonsymplectic 4-manifolds. This is detected by calculations of Seiberg-Witten invariants. The surgery in question can be performed on any 4-manifold which contains as a codimension 0 submanifold a punctured surface bundle over a punctured surface and a nontrivial loop in the base which has trivial monodromy. A starting point for another class of examples in this paper is a family of examples which show that the Parshin-Arakelov theorem for holomorphic Lefschetz fibrations is false in the symplectic category. Such families are constructed by means of knot surgery on elliptic surfaces. It is shown that for a fixed homeomorphism type X (of a simply connected elliptic surface) and a fixed integer $g \ge 3$, there are infinitely many genus g Lefschetz fibrations on nondiffeomorphic 4-manifolds, all homeomorphic to X. | |
| dc.identifier | https://arxiv.org/abs/math/0210206 | |
| dc.identifier | http://arxiv.org/abs/math/0210206 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65282 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R57 | |
| dc.title | Families of Simply Connected 4-Manifolds with the Same Seiberg-Witten Invariants | |
| dc.type | text |