Nilpotency of unstable \(K\)-theory
type: Item
instance of: scholarly article
title: Nilpotency of unstable \(K\)-theory
zbMATH Open document ID: 1117.55008
author: Hiroaki Hamanaka
published in: Topology and its Applications
publication date: 2007-04-18T00:00:00Z
review text: The author studies the nilpotency class of the homotopy set \([X,U(n)]\), where \(X\) is a finite connected \(CW\)-complex, and \(U(n)\) is the unitary group. Denoting \(N_{n,k}=\max\{nil[X,U(n)] \mid \dim X\leq 2n+k\}\), it is proved (sect. 2) that \(N_{n,k}\leq k+2\) and \(N_{n,k}\) is determined for \(k=0,1,2\) (sec. 3 and 4).
Mathematics Subject Classification ID: 55Q05
Mathematics Subject Classification ID: 55N15
zbMATH DE Number: 5144524
zbMATH Keywords: homotoy
zbMATH Keywords: unitary groups
zbMATH Keywords: \(K\)-theory
reviewed by: J. Remedios
MaRDI profile type: Publication
full work available at URL: j.topol.2005.04.017
OpenAlex ID: W2089472344
cites work: A note on the Samelson product in the classical groups
cites work: Homotopy nilpotency
cites work: On \([X,U(n)]\) when \(\dim X\) is \(2n\)
cites work: On \([X, U (n)]\) when \(dim X\) is \(2n+1\)
cites work: Nilpotence and finite H-spaces
cites work: Q4105006
cites work: THE HOMOTOPY GROUPS π2n+i(U(n)) FOR i=3, 4 AND 5.
cites work: Q5530411
DOI: 10.1016/J.TOPOL.2005.04.017
description: scientific article; zbMATH DE number 5144524