#### 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.

Notes on file formats
Brendan Owens

Department of Mathematics and Statistics

McMaster University

Hamilton, Ontario, Canada

Email: owensb@icarus.math.mcmaster.ca

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