Transparent pairs
Abstract
Let M be a closed orientable Riemannian surface. Consider an SO(3)-connection A and a Higgs field :M so(3). The pair (A,) naturally induces a cocycle over the geodesic flow of M. We classify (up to gauge transformations) cohomologically trivial pairs (A,) with finite Fourier series in terms of a suitable B\"acklund transformation. In particular, if M is negatively curved we obtain a full classification of SO(3)-transparent pairs.
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