On the ranks of homotopy groups of a space
type: Item
instance of: scholarly article
title: On the ranks of homotopy groups of a space
zbMATH Open document ID: 0691.55011
author: Kouyemon Iriye
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: For a simply connected space X of finite type and a prime p, let \(R_{\pi}\) and \(R_ H\) indicate the radii of convergence of the two power series \(P_{\pi}(X)=\sum (\dim \pi_ n(X)\otimes Z_ p)\cdot t^ n\) and \(P_ H(X)=\sum (\dim H_ n(\Omega X;Z_ p))\cdot t^ n,\) respectively. The author gives a partial answer to the Henn conjecture [\textit{H.-W. Henn}, Manuscr. Math. 56, 235-245 (1985; Zbl 0605.55009)]. Namely, \(\min \{1,R_{\pi}\}\leq R_ H\) for all simply connected spaces of finite type.
reviewed by: Yasukuni Furukawa
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55P35
zbMATH DE Number: 4131264
zbMATH Keywords: simply connected space
zbMATH Keywords: finite type
zbMATH Keywords: Henn conjecture
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195176851
OpenAlex ID: W2026653918
cites work: On the Pontryagin product in spaces of paths
cites work: On the growth of homotopy groups
cites work: Cohomologie modulo 2 des complexes d'Eilenberg-MacLane
cites work: A remark on a theorem of J. P. Serre
DOI: 10.2977/PRIMS/1195176851
description: scientific article; zbMATH DE number 4131264