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- Title
Modular representations and the homotopy of low rank p-local CW-complexes.
- Authors
Beben, Piotr; Wu, Jie
- 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 $${\widetilde H_*(X; \mathbb{Z}_p)}$$ of X, we use a decomposition of ΩΣ X due to the second author and computations in modular representation theory to show there are arbitrarily large integers i such that ΩΣ X is a homotopy retract of ΩΣ X. This implies the stable homotopy groups of Σ X are in a certain sense retracts of the unstable homotopy groups, and by a result of Stanley, one can confirm the Moore conjecture for Σ X. Under additional assumptions on $${\widetilde H_*(X; \mathbb{Z}_p)}$$, we generalize a result of Cohen and Neisendorfer to produce a homotopy decomposition of ΩΣ X that has infinitely many finite H-spaces as factors.
- Subjects
HOMOTOPY theory; SPACES of measures; FUNCTION spaces; TOPOLOGICAL spaces; MATHEMATICS
- Publication
Mathematische Zeitschrift, 2013, Vol 273, Issue 3/4, p735
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-012-1027-7