A remark on the homotopy type of the classifying space of certain gauge groups
type: Item
instance of: scholarly article
title: A remark on the homotopy type of the classifying space of certain gauge groups
zbMATH Open document ID: 0866.55019
author: Shuichi Tsukuda
published in: Journal of Mathematics of Kyoto University
publication date: 1996-11-27T00:00:00Z
review text: Let \(X\) be a closed simply connected 4-manifold and let \(P_k\) be the principal SU(2)-bundle over \(X\) with \(c_2(P_k)=k\) whose gauge group is denoted by \({\mathfrak g}_k\). In this paper, by examining the \(k\)-invariant of the localization of \(\text{Map}_k(X, HP^\infty)\) at prime \(p\), the author proves that a homotopy equivalence \(B{\mathfrak g}_k\simeq B{\mathfrak g}_m\) between classifying spaces implies \(gcd(k,p)=gcd(m,p)\) for any prime \(p\).
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 950583
zbMATH Keywords: 4-manifold
zbMATH Keywords: gauge group
zbMATH Keywords: localization
zbMATH Keywords: homotopy equivalence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518608
OpenAlex ID: W1556121841
DOI: 10.1215/KJM/1250518608
description: scientific article; zbMATH DE number 950583