Geometry & Topology 9 (2005) 1–93

DOI: 10.2140/gt.2005.9.1

arXiv: math.DG/0310047

Abstract

We study moduli spaces of Seiberg–Witten monopoles over spin^c Riemannian 4–manifolds with long necks and/or tubular ends. This first part discusses compactness, exponential decay, and transversality. As applications we prove two vanishing theorems for Seiberg–Witten invariants.

Keywords

Floer homology, Seiberg–Witten, Bauer–Furuta, compactness, monopoles

Mathematical Subject Classification

Primary: 57R58

Secondary: 57R57

References

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Publication

Received: 9 October 2003
Revised: 1 December 2004
Accepted: 29 September 2004
Published: 17 December 2004
Proposed: Dieter Kotschick
Seconded: Simon Donaldson, Tomasz Mrowka

Authors