Algebraic & Geometric Topology

Stable functorial decompositions of $F(\mathbb{R}^{n+1},j)^{+}\wedge_{\Sigma_j}X^{(j)}$

Jie Wu and Zihong Yuan

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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(n+1,j)+ ΣjX(j).

Article information

Algebr. Geom. Topol., Volume 17, Number 2 (2017), 895-915.

Received: 9 September 2015
Revised: 18 April 2016
Accepted: 30 September 2016
First available in Project Euclid: 19 October 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P35: Loop spaces
Secondary: 55P48: Loop space machines, operads [See also 18D50] 55P65: Homotopy functors

Snaith splitting iterated loop suspension functorial homotopy decomposition coalgebra-split sub-Hopf algebra


Wu, Jie; Yuan, Zihong. Stable functorial decompositions of $F(\mathbb{R}^{n+1},j)^{+}\wedge_{\Sigma_j}X^{(j)}$. Algebr. Geom. Topol. 17 (2017), no. 2, 895--915. doi:10.2140/agt.2017.17.895.

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