Coincidences of multiple fibre-preserving maps

Abstract In this paper we study the following problem: given X ↪ M → B and Y ↪ N → B smooth fibre bundles over B and f 1 , … , f k : M → N fibre-preserving maps, is it possible to deform ( f 1 , … , f k ) ∼ ( f 1 ′ , … , f k ′ ) via a fibrewise homotopy over B such that the set of coincidence points of f 1 ′ , … , f k ′ : M → N is empty? We study this question making use of obstruction theory.