2010/02/19 by Piotr Beben, Jie Wu, Beben, Piotr +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1002.3752
openalex publication_date 2010/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fix an odd prime p and let X be the p-localization of a finite suspended CW-complex. Given certain conditions on the reduced mod-p homology H_*(X;\zmodp) of X, we use a decomposition of ΩΣX due to the second author and computations in modular representation theory to show there are arbitrarily large integers i such that ΩΣi X is a homotopy retract of ΩΣX. This implies the stable homotopy groups of ΣX are in a certain sense retracts of the unstable homotopy groups, and by a result of Stanley, one can confirm the Moore conjecture for ΣX. Under additional assumptions on H_*(X;\zmodp), we generalize a result of Cohen and Neisendorfer to produce a homotopy decomposition of ΩΣX that has infinitely many finite H-spaces as factors.