= Coulomb slice for unitary connections
{c}
{title2=$d_A^*a=0$}
Near a fixed connection $A$, impose $d_A^*a=0$ on perturbations. The linearized gauge-fixing equation is $d_A^*d_A\xi$, invertible on the orthogonal complement of its parallel kernel. In Sobolev completions above the multiplication threshold, the implicit function theorem gives a local slice; its remaining identifications are by the compact stabilizer of $A$. This reduces the gauge quotient to a finite-dimensional Kuranishi model when the curvature equation is elliptic.
// Destination: geometry-and-topology.bigb
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