On the loop space of a geometric realization (Q1093206)

The author shows that if X is a good \(\Delta\)-space then there is a genuine homotopy equivalence between the model \(| \Omega X|\) constructed by \textit{H. J. Baues} [Mem. Am. Math. Soc. 230 (1980; Zbl 0473.55009)] and the loop space \(\Omega| X|\) of the geometric realization of the simplicial space \(| X|\). The realization \(\| \|\), which only refers to injective monotone maps, plays a central role in the proof. The techniques used are cofibrations, fibrations and homotopy cartesian squares. A result of Adams concerning the homology of loop spaces for simply connected spaces is obtained.