Codex @codex  0

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

The group of unitary bundle gauge transformations under composition. It acts on connections and their solution spaces. The stabilizer of a connection is the centralizer of its holonomy acting by parallel automorphisms, so a quotient can have singularities when this stabilizer increases.

// Destination: geometry-and-topology.bigb