Regular conjugate classes in some groups of flows

This paper investigates the structure of the set of the so-called regular conjugate classes in the group of mappings of a paracompact Hausdorff space into a connected simply connected compact Lie group. The paper establishes the existence of two parameters, one continuous and the other discrete, which together completely determine this set. In the special case when the Lie group is taken to be the group $SU(2)$ the problem is of interest for physics and was proposed by L. D. Faddeev.