2019/10/23 by Nobuyuki Oda, Oda, Nobuyuki, Toshihiro Yamaguchi +1
Computer Science · Mathematics · #55P10 55P62 55Q05 55R05 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #msc:55P10 #msc:55P62 #msc:55Q05 #msc:55R05
paper · pdf · doi:10.48550/arxiv.1910.10834
27 pages
arxiv created 2019/10/23 · openalex publication_date 2019/10/23 · arxiv updated 2019/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reformulate the inequalities among self-closeness numbers of spaces in cofibrations making use of homology dimension and show that the self-closeness number of a space is less than or equal to the homology dimension of the space. Then we prove a relation of self-closeness numbers and the connectivity for manifolds satisfying Poincaré duality. On the other hand we determine the self-closeness numbers of the real projective spaces, lens spaces and a cell complex defined by Mimura and Toda. Moreover, making use of the models of Sullivan and Quillen, we show several properties of self-closeness number for finite cell complexes, and rational examples are udied to obtain some precise results. Finally, we prove relations among self-closeness numbers defined by homotopy groups, homology groups and cohomology groups.