Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00209-012-1027-7
Title: Modular representations and the homotopy of low rank p-local CW-complexes
Authors: Beben, P.
Wu, J. 
Keywords: Finite CW-complexes
Loop space decompositions
Modular representations
Issue Date: Apr-2013
Citation: Beben, P., Wu, J. (2013-04). Modular representations and the homotopy of low rank p-local CW-complexes. Mathematische Zeitschrift 273 (3-4) : 735-751. ScholarBank@NUS Repository. https://doi.org/10.1007/s00209-012-1027-7
Abstract: 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 H̃*(X; ℤp) 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 ΩΣiX 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 H̃*(X; ℤp), we generalize a result of Cohen and Neisendorfer to produce a homotopy decomposition of ΩΣX that has infinitely many finite H-spaces as factors. © 2012 Springer-Verlag.
Source Title: Mathematische Zeitschrift
URI: http://scholarbank.nus.edu.sg/handle/10635/103556
ISSN: 00255874
DOI: 10.1007/s00209-012-1027-7
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