Jan Bohr (Bonn)
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DEN 111
Abstract: A unitary connection on the 2-sphere is called transparent, if its parallel along all great circles is the identity. In the scalar case this is equivalent to the connection being odd up to gauge, but for higher ranks the situation is more intricate. Mason proposed a classification of transparent connections on the 2-sphere in terms of complex geometric data on \$\mathbb{CP}^2\$. In the talk I will discuss a generalisation of this classification that incorporates unitary pairs (connection + matrix field), as well as other closed Riemannian surfaces. The role of \$\mathbb{CP}^2\$ is then played by transport twistor space, a degenerate complex surface tailored to the geodesic flow, or (when available) its desingularisation.