Instantons on cylindrical manifolds and stable bundles

Owens, Brendan¹

¹ Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada

Geometry & topology, Tome 5 (2001) no. 2, pp. 761-797.

Résumé

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

Détail

DOI : 10.2140/gt.2001.5.761

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

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