Decompositions of certain loop spaces.
The author studies the decomposition of loop spaces of: (1) mapping cones of maps between wedge products of Moore spaces; and (2) spaces he calls \(\mathbb{Z}/p\)-conformal which were defined by \textit{J. A. Neisendorfer} and \textit{T. Miller} [Illinois J. Math. 22, 565-579 (1978; Zbl 0396.55011)]. For the mapping cone \(C_f\) where \(f\) is a map between finite wedge products of Moore spaces of type \(p^n\), the loop space \(\Omega C_f\) has the homotopy type of a weak product space of Cohn-Moore-Neisendorfer factors under some dimensionality hypotheses and a condition on the homology of \(\Omega C_f\). For certain coformal CW complexes, the loop space is homotopy equivalent to the weak product of factor spaces of the CMF type or of \(p\)-local spheres and their loop spaces. A corollary of these results states that the Moore exponent conjecture is true for the classes of spaces for which the above results are true.
scientific article; zbMATH DE number 2005933
scientific article