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The homotopy decomposition of the suspension of a non-simply-connected five-manifold

Part of: Differential topology Homotopy theory

Published online by Cambridge University Press:  17 April 2024

Pengcheng Li  and
Zhongjian Zhu
Pengcheng Li
Affiliation:
Department of Mathematics, School of Sciences, Great Bay University, Dongguan, Guangdong 523000, China (lipcaty@outlook.com)
Zhongjian Zhu
Affiliation:
College of Mathematics and Physics, Wenzhou University, Wenzhou, Zhejiang 325035, China (zhuzhongjian@amss.ac.cn)
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Abstract

In this paper we determine the homotopy types of the reduced suspension space of certain connected orientable closed smooth $five$-manifolds. As applications, we compute the reduced $K$-groups of $M$ and show that the suspension map between the third cohomotopy set $\pi ^3(M)$ and the fourth cohomotopy set $\pi ^4(\Sigma M)$ is a bijection.

Keywords

homotopy typesuspensionfive-manifoldscohomotopy sets

MSC classification

Primary: 55P15: Classification of homotopy type 55P40: Suspensions 57R19: Algebraic topology on manifolds
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 29
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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