Instantons on cylindrical manifolds and stable bundles

Abstract

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(2)-instantons over the cylinder Sigma \times S^1 \times R, and rank 2 holomorphic bundles over S whose restrictions to the divisors at infinity are stable.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper24.abs.html

Cited by in corpus (3)

• Hermitian Yang-Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds
• Spatially periodic instantons: Nahm transform and moduli
• The extended Bogomolny equations with generalized Nahm pole boundary conditions, II