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

Abstract

We classify principal O( n )-bundles over 4-dimensional closed manifolds for n = 3 and n ≥ 5 and SO(2 n )-bundles over 2 n -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.