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

2023/11/28 by Pengcheng Li, Li, Pengcheng, Zhongjian Zhu +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.16642

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 π³(M) and the fourth cohomotopy set π⁴(ΣM) is a bijection.

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