The suspension of a 4-manifold and its applications

2019/09/24 by Tseleung So, So, Tseleung, Stephen Theriault +1
Computer Science · Mathematics · #55P40 (Primary) #57N65 #81T13 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1909.11129

openalex publication_date 2019/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a smooth, orientable, closed, connected 4-manifold and suppose that H₁(M;ℤ) is finitely generated and has no 2-torsion. We give a homotopy decomposition of the suspension of M in terms of spheres, Moore spaces and ΣℂP². This is used to calculate any reduced generalized cohomology theory of M as a group and to determine the homotopy types of certain current groups and gauge groups.

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