Geometry & Topology

Instantons on cylindrical manifolds and stable bundles

Brendan Owens

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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.

Article information

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

Received: 23 February 2001
Revised: 25 October 2001
Accepted: 5 October 2001
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]
Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 57R58: Floer homology 14J80: Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)

Anti-self-dual connection stable bundle product ruled surface


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

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