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 $\Sigma$ be a smooth complex curve, and let $S$ be the product ruled surface $\Sigma ×ℂ{P}^{1}$. We prove a correspondence conjectured by Donaldson between finite energy $U\left(2\right)$–instantons over $\Sigma ×{S}^{1}×ℝ$, and rank 2 holomorphic bundles over $S$ whose restrictions to $\Sigma ×\left\{0\right\},\Sigma ×\left\{\infty \right\}$ are stable.

Keywords
Anti-self-dual connection, stable bundle, product ruled surface
Mathematical Subject Classification 2000
Primary: 53C07
Secondary: 14J60, 57R58, 14J80
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