2021/07/15 by Yichen Tong, Tong, Yichen
Mathematics · #55P10 #55S37 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P10 #msc:55S37
paper · pdf · doi:10.48550/arxiv.2107.07109
18 pages
arxiv created 2021/07/15 · openalex publication_date 2021/07/15 · arxiv updated 2021/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The self-closeness number NE(X) of a space X is the least integer k such that any self-map is a homotopy equivalence whenever it is an isomorphism in the n-th homotopy group for each n≤ k. We discuss the self-closeness numbers of certain non-simply-connected X in this paper. As a result, we give conditions for X such that NE(X)=NE(\widetildeX), where \widetildeX is the universal covering space of X.