Homotopy types of suspended 4–manifolds

Li, Pengcheng

doi:10.2140/agt.2024.24.2933

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Homotopy types of suspended $4$–manifolds

Pengcheng Li

Algebraic & Geometric Topology 24 (2024) 2933–2956

DOI: 10.2140/agt.2024.24.2933

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 $Σ^{2} M$ as wedge sums of some elementary $A_{3}^{3}$ –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 $Σ^{2} M$ to desuspend to that of $Σ M$ .

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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Volume 24, issue 5 (2024)