Lionel Mason
(University of Oxford, UK)
Transparent connections on the plane and sphere and Ward's 2+1 Chiral Model
Transparent connections on the plane and sphere and Ward's 2+1 Chiral Model
Transparent connections on the projective plane and sphere are those with zero holonomy along lines or great circles. They are characterised in terms of homolomorphic vector bundles on the complex projective plane. This leads to a complete description in terms of algebraic data of those on the plane, and an analytic description in terms of a Riemann-Hilbert problem on the sphere. These can then be interpreted as characteristic data for Ward's chiral model. The lump solutions are then characterised as transparent connections on the plane, but generic solutions as those on the sphere.