Classification of exterior and proper fibrations

Abstract

As in the classical setting, we classify a large class of exterior fibrations in the based exterior homotopy category. More precisely, the fibration sequences F → E → X F\to E\to X of path-connected based exterior CW-complexes are in bijective correspondence with the based exterior homotopy classes of maps from X X to a universal exterior CW-complex Y F Y_F . As a result we classify proper fibrations between CW-complexes.