Reducible SU2 connection
= Reducible SU2 connection
{title2=$E=L\oplus L^{-1}$}
An $SU(2)$ connection whose holonomy lies in a maximal circle, equivalently one preserving a splitting $E=L\oplus L^{-1}$. If its holonomy is the entire circle, parallel adjoint sections are exactly the one-real-dimensional diagonal Lie algebra. The off-diagonal real plane is the underlying real bundle of $L^2$ and has circle weight two.
// Destination: geometry-and-topology.bigb