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

Jie Wu and Zihong Yuan

Algebraic & Geometric Topology 17 (2017) 895–915
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(n+1,j)+ ΣjX(j).

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Keywords
Snaith splitting, iterated loop suspension, functorial homotopy decomposition, coalgebra-split sub-Hopf algebra
Mathematical Subject Classification 2010
Primary: 55P35
Secondary: 55P48, 55P65
References
Publication
Received: 9 September 2015
Revised: 18 April 2016
Accepted: 30 September 2016
Published: 14 March 2017
Authors
Jie Wu
Department of Mathematics
National University of Singapore
Block S17 (SOC1), 06-02
10 Lower Kent Ridge Road
Singapore 119076
Singapore
http://www.math.nus.edu.sg/~matwujie
Zihong Yuan
Institute for Infocomm Research
1 Fusionopolis Way
#21-01 Connexis South Tower
Singapore 138632
Singapore