Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Monopoles over 4–manifolds containing long necks I

Kim A Frøyshov

Geometry & Topology 9 (2005) 1–93

arXiv: math.DG/0310047

Abstract

We study moduli spaces of Seiberg–Witten monopoles over spinc 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 2000
Primary: 57R58
Secondary: 57R57
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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
Kim A Frøyshov
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
D-33501 Bielefeld
Germany