## Algebraic & Geometric Topology

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

#### Abstract

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 $F(ℝn+1,j)+ ∧ΣjX(j)$.

#### Article information

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

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

https://projecteuclid.org/euclid.agt/1508431448

Digital Object Identifier
doi:10.2140/agt.2017.17.895

Mathematical Reviews number (MathSciNet)
MR3623676

Zentralblatt MATH identifier
1361.55011

Subjects
Primary: 55P35: Loop spaces

#### Citation

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. https://projecteuclid.org/euclid.agt/1508431448

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