Equivariant self equivalences of principal fibre bundles

Abstract

Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G. For principal fibre bundle (E,p, E/G;G) and (E/H,p′, E/G;G/H), the relation between autg(E) (resp. aut g * (E)) and aut G H (E/H) (resp. aut g H /*)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group Fg(E) (resp. EG(E)) while the group FG/H(E/H) is known.