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Homotopy types of suspended $4$–manifolds

Pengcheng Li

Algebraic & Geometric Topology 24 (2024) 2933–2956
Abstract

Given a closed, smooth, connected, orientable 4–manifold M whose integral homology groups can have 2–torsion, we determine the homotopy decomposition of the double suspension Σ2M as wedge sums of some elementary A33–complexes which are 2–connected finite complexes of dimension at most 6. Furthermore, we utilize the Postnikov square (or equivalently Pontryagin square) to find sufficient conditions for the homotopy decompositions of Σ2M to desuspend to that of ΣM.

Keywords
homotopy type, suspension, four-manifolds, $\mathbf{A}_3^3$–complexes
Mathematical Subject Classification
Primary: 55P15, 55P40, 57N65
References
Publication
Received: 8 March 2023
Revised: 9 May 2023
Accepted: 9 June 2023
Published: 19 August 2024
Authors
Pengcheng Li
Department of Mathematics, School of Sciences
Great Bay University
Dongguan
Guangdong
China
https://lipcaty.github.io

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