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2008 The decomposition of the loop space of the mod $2$ Moore space
Jelena Grbić, Paul Selick, Jie Wu
Algebr. Geom. Topol. 8(2): 945-951 (2008). DOI: 10.2140/agt.2008.8.945


In 1979 Cohen, Moore and Neisendorfer determined the decomposition into indecomposable pieces, up to homotopy, of the loop space on the mod p Moore space for primes p>2 and used the results to find the best possible exponent for the homotopy groups of spheres and for Moore spaces at such primes. The corresponding problems for p=2 are still open. In this paper we reduce to algebra the determination of the base indecomposable factor in the decomposition of the mod 2 Moore space. The algebraic problems involved in determining detailed information about this factor are formidable, related to deep unsolved problems in the modular representation theory of the symmetric groups. Our decomposition has not led (thus far) to a proof of the conjectured existence of an exponent for the homotopy groups of the mod 2 Moore space or to an improvement in the known bounds for the exponent of the 2–torsion in the homotopy groups of spheres.


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Jelena Grbić. Paul Selick. Jie Wu. "The decomposition of the loop space of the mod $2$ Moore space." Algebr. Geom. Topol. 8 (2) 945 - 951, 2008.


Received: 26 December 2007; Revised: 28 March 2008; Accepted: 23 April 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1148.55004
MathSciNet: MR2443103
Digital Object Identifier: 10.2140/agt.2008.8.945

Primary: 55P35
Secondary: 16W30

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.8 • No. 2 • 2008
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