## Geometry & Topology

### Instantons on cylindrical manifolds and stable bundles

Brendan Owens

#### Abstract

Let $Σ$ be a smooth complex curve, and let $S$ be the product ruled surface $Σ×ℂP1$. We prove a correspondence conjectured by Donaldson between finite energy $U(2)$–instantons over $Σ×S1×ℝ$, and rank 2 holomorphic bundles over $S$ whose restrictions to $Σ×{0},Σ×{∞}$ are stable.

#### Article information

Source
Geom. Topol., Volume 5, Number 2 (2001), 761-797.

Dates
Revised: 25 October 2001
Accepted: 5 October 2001
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883043

Digital Object Identifier
doi:10.2140/gt.2001.5.761

Mathematical Reviews number (MathSciNet)
MR1871404

Zentralblatt MATH identifier
1069.53029

#### Citation

Owens, Brendan. Instantons on cylindrical manifolds and stable bundles. Geom. Topol. 5 (2001), no. 2, 761--797. doi:10.2140/gt.2001.5.761. https://projecteuclid.org/euclid.gt/1513883043

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