Suspension Splitting and Cohomotopy Sets of Simply Connected 7-manifolds

2022/08/28 by Ruizhi Huang, Pengcheng Li, Huang, Ruizhi +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2208.13145

openalex publication_date 2022/08/28 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

Let M be a closed simply connected 7-manifold. In this paper we establish homotopy decompositions of the reduced suspension space ΣM into a wedge sum of simpler spaces when localized at a set of primes. These decompositions are applied to study the cohomotopy sets π^k(M) and the p-local cohomotopy sets π⁴(M;ℤ_(p)).

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