Stable functorial decompositions of F(ℝn+1,j)+ ∧ΣjX(j)

Wu, Jie; Yuan, Zihong

doi:10.2140/agt.2017.17.895

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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

DOI: 10.2140/agt.2017.17.895

Abstract

We first construct a functorial homotopy retract of $Ω^{n + 1} Σ^{n + 1} X$ 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 $F {(ℝ^{n + 1}, j)}^{+} \land_{Σ_{j}} X^{(j)}$ .

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

Volume 17, issue 2 (2017)