Geodesic
Stable functorial decompositions of F(ℝn+1,j)+ ∧ΣjX(j)
Wu, Jie1 ; Yuan, Zihong2
1Department of Mathematics, National University of Singapore, Block S17 (SOC1), 06-02, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
2Institute for Infocomm Research, 1 Fusionopolis Way, #21-01 Connexis South Tower, Singapore 138632, Singapore
Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 895-915
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We first construct a functorial homotopy retract of Ωn+1Σn+1X for each natural coalgebra-split sub-Hopf algebra of the tensor algebra. Then, by computing their homology, we find a collection of stable functorial homotopy retracts of F(ℝn+1,j)+ ∧ΣjX(j).

DOI : 10.2140/agt.2017.17.895
Classification : 55P35, 55P48, 55P65
Keywords: Snaith splitting, iterated loop suspension, functorial homotopy decomposition, coalgebra-split sub-Hopf algebra

Wu, Jie  1   ; Yuan, Zihong  2

1 Department of Mathematics, National University of Singapore, Block S17 (SOC1), 06-02, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
2 Institute for Infocomm Research, 1 Fusionopolis Way, #21-01 Connexis South Tower, Singapore 138632, Singapore 
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Wu, Jie; Yuan, Zihong. Stable functorial decompositions of F(ℝn+1,j)+ ∧ΣjX(j). Algebraic and Geometric Topology, Tome 17 (2017) no. 2, pp. 895-915. doi: 10.2140/agt.2017.17.895

[1] A Bahri, M Bendersky, F R Cohen, S Gitler, The polyhedral product functor: a method of decomposition for moment-angle complexes, arrangements and related spaces, Adv. Math. 225 (2010) 1634 | DOI

[2] C F Bödigheimer, Stable splittings of mapping spaces, from: "Algebraic topology" (editors H R Miller, D C Ravenel), Lecture Notes in Math. 1286, Springer (1987) 174 | DOI

[3] F R Cohen, The homology of Cn+1–spaces, n ≥ 0, from: "The homology of iterated loop spaces" (editors F R Cohen, T J Lada, J P May), Lecture Notes in Mathematics 533, Springer (1976) 207 | DOI

[4] F R Cohen, J P May, L R Taylor, Splitting of certain spaces CX, Math. Proc. Cambridge Philos. Soc. 84 (1978) 465 | DOI

[5] F R Cohen, J P May, L R Taylor, Splitting of some more spaces, Math. Proc. Cambridge Philos. Soc. 86 (1979) 227 | DOI

[6] N Dobrinskaya, Loops on polyhedral products and diagonal arrangements, preprint (2009)

[7] J Y Li, F C Lei, J Wu, Module structure on Lie powers and natural coalgebra-split sub-Hopf algebras of tensor algebras, Proc. Edinb. Math. Soc. 54 (2011) 467 | DOI

[8] J P May, L R Taylor, Generalized splitting theorems, Math. Proc. Cambridge Philos. Soc. 93 (1983) 73 | DOI

[9] J Mccleary, A user’s guide to spectral sequences, 58, Cambridge University Press (2001)

[10] P Selick, J Wu, On natural coalgebra decompositions of tensor algebras and loop suspensions, 701, Amer. Math. Soc. (2000) | DOI

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

[12] V P Snaith, A stable decomposition of ΩnSnX, J. London Math. Soc. 7 (1974) 577 | DOI

[13] Z H Yuan, Functorial homotopy decompositions of iterated loop suspensions, PhD thesis, National University of Singapore (2014)

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