Volume 5, issue 2 (2001)

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Instantons on cylindrical manifolds and stable bundles

Brendan Owens

Geometry & Topology 5 (2001) 761–797

arXiv: math.DG/0010106

Abstract

Let Σ be a smooth complex curve, and let S be the product ruled surface Σ × P1. We prove a correspondence conjectured by Donaldson between finite energy U(2)–instantons over Σ × S1 × , and rank 2 holomorphic bundles over S whose restrictions to Σ ×{0},Σ ×{} are stable.

Keywords
Anti-self-dual connection, stable bundle, product ruled surface
Mathematical Subject Classification 2000
Primary: 53C07
Secondary: 14J60, 57R58, 14J80
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Publication
Received: 23 February 2001
Revised: 25 October 2001
Accepted: 5 October 2001
Published: 25 October 2001
Proposed: Simon Donaldson
Seconded: John Morgan, Tomasz Mrowka
Authors
Brendan Owens
Department of Mathematics and Statistics
McMaster University
Hamilton
Ontario
Canada