GT Vol 9 (2005) Paper 1 (Abstract)

Geometry & Topology, Vol. 9 (2005) Paper no. 1, pages 1--93.

Monopoles over 4-manifolds containing long necks, I

Kim A Froyshov

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

AMS subject classification. Primary: 57R58. Secondary: 57R57.

DOI: 10.2140/gt.2005.9.1

E-print: arXiv:math.DG/0310047

Submitted to GT on 9 October 2003. (Revised 1 December 2004.) Paper accepted 29 September 2004. Paper published 17 December 2004.

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Kim A Froyshov
Fakultaeat fuer Mathematik, Universitaet Bielefeld
Postfach 100131, D-33501 Bielefeld, Germany
Email: froyshov@mathematik.uni-bielefeld.de

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