Classification of exterior and proper fibrations

García-Calcines, J.; García-Díaz, P.; Murillo, A.

doi:10.1090/proc/14956

Classification of exterior and proper fibrations
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by J. M. García-Calcines, P. R. García-Díaz and A. Murillo PDF

Proc. Amer. Math. Soc. 148 (2020), 3175-3185 Request permission

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 $F\to E\to X$ of path-connected based exterior CW-complexes are in bijective correspondence with the based exterior homotopy classes of maps from $X$ to a universal exterior CW-complex $Y_F$. As a result we classify proper fibrations between CW-complexes.

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