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Invariant Sp(1)-instantons on S 2 × S 2

Abstract

In this paper all (anti)self-dual invariant connections on homogeneous quaternionic line bundles over S 2 × S 2 are calculated and described in terms of the isotropy homomorphism of the bundle using Wang's theorem. These are the canonical connections on bundles with an ‘(anti)symmetric twist’ and an S 1-parametrized family of flat structures on bundles with a ‘simple twist’.

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Unger, F.R. Invariant Sp(1)-instantons on S 2 × S 2 . Geom Dedicata 23, 365–368 (1987). https://doi.org/10.1007/BF00181319

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  • DOI: https://doi.org/10.1007/BF00181319

Keywords

  • Line Bundle
  • Canonical Connection
  • Flat Structure
  • Invariant Connection
  • Quaternionic Line