Instantons on cylindrical manifolds and stable bundles

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

Keywords

Anti-self-dual connection, stable bundle, product ruled surface

Mathematical Subject Classification 2000

Primary: 53C07

Secondary: 14J60, 57R58, 14J80

References

Forward citations

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

Volume 5, issue 2 (2001)

Brendan Owens