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arXiv · 2311.16642

The homotopy decomposition of the suspension of a non-simply-connected $5$-manifold

Pengcheng Li·Zhongjian Zhu
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Abstract

In this paper we determine the homotopy types of the reduced suspension space of certain connected orientable closed smooth $5$-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.

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Pengcheng Li, Zhongjian Zhu. 2023-11-28. The homotopy decomposition of the suspension of a non-simply-connected $5$-manifold. https://arxiv.org/abs/2311.16642

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