Fake Lie groups and maximal tori. II
type: Item
instance of: scholarly article
title: Fake Lie groups and maximal tori. II
zbMATH Open document ID: 0697.55007
DOI: 10.1007/BF01444557
author: Dietrich Notbohm
author: Larry Smith
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164759
review text: [Part I is reviewed above (see Zbl 0697.55006).] A finite loop space X is called a fake Lie group of type G, where G is a compact connected Lie group, if the classifying spaces BX and BG have the same genus. (Recall that two nilpotent spaces of finite type \(Y'\), \(Y''\) are said to have the same genus if their p-localizations are homotopy equivalent for all primes.) Rector's maximal torus theorem may be interpreted as using the existence of a maximal torus for \({\mathbb{S}}p(1)\) to distinguish \({\mathbb{S}}p(1)\) from a fake \({\mathbb{S}}p(1)\). In this note we prove the analog of Rector's theorem for \({\mathbb{U}}(2)\). As a bonus we are able to characterize B\({\mathbb{U}}(2)\) up to homotopy type by its K-theory.
Mathematics Subject Classification ID: 55P35
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 4143032
zbMATH Keywords: finite loop space
zbMATH Keywords: fake Lie group
zbMATH Keywords: compact connected Lie group
zbMATH Keywords: classifying spaces
zbMATH Keywords: genus
zbMATH Keywords: p-localizations
zbMATH Keywords: maximal torus
zbMATH Keywords: U(2)
zbMATH Keywords: BU(2)
zbMATH Keywords: K-theory
Wikidata QID: Q115393537
MaRDI profile type: Publication
cites work: On the mod p torus theorem of John Hubbuck
cites work: POWER OPERATIONS IN K-THEORY
cites work: Homotopy limits, completions and localizations
cites work: On homotopy commutative H-spaces
cites work: Self-maps of classifying spaces of compact simple Lie groups
cites work: A cohomological proof of the torus theorem
cites work: THE HOMOTOPY CLASSIFICATION OF SELF-MAPS OF INFINITE QUATERNIONIC PROJECTIVE SPACE
cites work: Fake Lie groups with maximal tori. IV
cites work: Fake Lie groups and maximal tori. I
cites work: Subgroups of finite dimensional topological groups
cites work: A classification theorem for fibre spaces
cites work: Applications of minimal simplicial groups
OpenAlex ID: W4235181747
description: scientific article; zbMATH DE number 4143032