#### Volume 5, issue 2 (2001)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
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