On the gauge orbit types for theories with classical compact gauge group

We classify principal O(n)-bundles over 4-dimensional closed manifolds for n = 3 and n ≥ 5 and SO(2n)-bundles over 2n-dimensional closed manifolds. This is part of a program to determine the orbit types of the action of the group of local gauge transformations on gauge potentials for an arbitrary compact classical gauge group and an arbitrary 4-dimensional space-time.