Geometry & Topology, Vol. 5 (2001) Paper no. 24, pages 761--797.

Instantons on cylindrical manifolds and stable bundles

Brendan Owens

Abstract. Let Sigma be a smooth complex curve, and let S be the product ruled surface Sigma \times CP^1. We prove a correspondence conjectured by Donaldson between finite energy U(2)-instantons over the cylinder Sigma \times S^1 \times R, and rank 2 holomorphic bundles over S whose restrictions to the divisors at infinity are stable.

Keywords. Anti-self-dual connection, stable bundle, product ruled surface

AMS subject classification. Primary: 53C07. Secondary: 14J60, 57R58, 14J80.

DOI: 10.2140/gt.2001.5.761

E-print: arXiv:math.DG/0010106

Submitted to GT on 23 February 2001. (Revised 25 October 2001.) Paper accepted 5 October 2001. Paper published 25 October 2001.

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Brendan Owens
Department of Mathematics and Statistics
McMaster University
Hamilton, Ontario, Canada
Email: owensb@icarus.math.mcmaster.ca

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