Based unitary gauge group
= Based unitary gauge group
{title2=$\mathcal G_x=\{u:u(x)=1\}$}
The subgroup of <unitary bundle gauge transformations> equal to the identity at a chosen framed base point. Quotienting flat connections by this subgroup retains the full <flat holonomy representation>; quotienting by the whole group also divides by simultaneous conjugation.
// Destination: geometry-and-topology.bigb