Coincidence points of principal bundles

Abstract

Let p: E→ B be a principal G-bundle where G is a compact connected Lie group, p′: E′→ B′ be a fibre bundle and f, g: E′→ E be fibre-preserving maps over a map h: B′→ B. If the Lefschetz number for the restriction of f and g on a fibre is not zero, we give the number of nonempty Nielsen classes over h for f and g as well as the topological dimension of each class.