The Seiberg-Witten theory of homology 3-spheres
| dc.creator | Chen, Weimin | |
| dc.date | 1997-03-16 | |
| dc.date | 2000-02-01 | |
| dc.date.accessioned | 2026-07-07T08:59:13Z | |
| dc.date.available | 2026-07-07T08:59:13Z | |
| dc.description | In this thesis we study the Seiberg-Witten theory of an oriented homology 3-sphere. The goal is to extract topological invariants - the Seiberg-Witten invariants - by counting the solutions to the Seiberg-Witten equations on the manifold. The first question we consider is whether the Seiberg-Witten invariants depend on the geometric or analytic data involved in their definition. In the first main result of this thesis, we completely determine the dependence of the Seiberg-Witten invariants on the data involved in their definition. In particular, we show that even for the simplest manifold, the 3-sphere $S^3$, the Seiberg-Witten invariants take infinitely many different values. The rest of this thesis is devoted to understanding the Seiberg-Witten invariants in a specific geometric setting - the surgery setting. In that context we prove a gluing formula, which identifies the Seiberg-Witten invariants as certain ``homological intersection numbers''. | |
| dc.description | An incorrect statement (the surgery formula) in an earlier version is removed. This version is the PhD thesis of the author | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9703009 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9703009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147628 | |
| dc.subject | Differential Geometry | |
| dc.title | The Seiberg-Witten theory of homology 3-spheres | |
| dc.type | text |