Geodesic
Decomposition of loop spaces and periodic problem on π∗
Chen, Weidong1 ; Wu, Jie2
1Centre for Maritime Studies, National University of Singapore, 12 Prince George’s Park, Singapore 118411, Singapore
2Department of Mathematics, National University of Singapore, Block S17 (SOC1), 06-02, 10, Lower Kent Ridge Road, Singapore 119076, Singapore
Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3245-3260
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We provide a family of spaces localized at 2, whose stable homotopy groups are summands of their unstable homotopy groups. Applications to mod 2 Moore spaces are given.

DOI : 10.2140/agt.2013.13.3245
Classification : 55P35, 55Q10, 55Q52
Keywords: loop spaces, stable homotopy groups, homotopy groups of 2–cell complexes

Chen, Weidong  1   ; Wu, Jie  2

1 Centre for Maritime Studies, National University of Singapore, 12 Prince George’s Park, Singapore 118411, Singapore
2 Department of Mathematics, National University of Singapore, Block S17 (SOC1), 06-02, 10, Lower Kent Ridge Road, Singapore 119076, Singapore 
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Chen, Weidong; Wu, Jie. Decomposition of loop spaces and periodic problem on π∗. Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3245-3260. doi: 10.2140/agt.2013.13.3245

[1] P Beben, J Wu, Modular representations and the homotopy of low rank $p$–local CW–complexes, Math. Z. 273 (2013) 735

[2] F R Cohen, J Wu, A remark on the homotopy groups of $\Sigma^n\mathbf{R}\mathrm{P}^2$, from: "The Čech centennial" (editors M Cenkl, H Miller), Contemp. Math. 181, Amer. Math. Soc. (1995) 65

[3] H Freudenthal, Über die Klassen der Sphärenabbildungen, I: Gro\ss e Dimensionen, Compositio Math. 5 (1938) 299

[4] P Selick, J Wu, On functorial decompositions of self-smash products, Manuscripta Math. 111 (2003) 435

[5] P Selick, J Wu, The functor $A^{{\mathrm{min}}}$ on $p$–local spaces, Math. Z. 253 (2006) 435

[6] J Wu, On combinatorial calculations for the James–Hopf maps, Topology 37 (1998) 1011

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