of some point 1 ∈ ∈ P ~ ~ x 0 of a group bundle P ~ ~ → → X . It is called the pointed gauge group. This group acts freely on a space of principal connections. Obviously, G ( X ) / G 0 ( X ) = G . One also introduces the effective gauge group G ¯ ¯ ( X ) = G ( X ) / Z where Z is the center of a gauge group G ( X ) . This group G ¯ ¯ ( X ) acts freely on a space of irreducible principal connections.