Covering space semigroups and retracts of compact Lie groups
type: Item
instance of: scholarly article
title: Covering space semigroups and retracts of compact Lie groups
zbMATH Open document ID: 1359.22004
author: John R. Martin
author: Karl H. Hofmann
published in: Journal of Geometry
publication date: 2017-02-02T00:00:00Z
review text: Let \(B\) be a compact connected Lie group, \(N\) a finite central subgroup of \(B\) and \(f:B\to B/N\) be the quotient morphism of \(B\). The mapping cylinder \(MC(f)\) associated with \(f\) is a compact monoid called covering space semigroup. A covering space semigroup is not in general a manifold but it does admit a manifold boundary. The main theorem of this paper (Theorem 3.6) states that for a compact connected Lie group \(B\) having the central circle group as a direct factor there exist infinitely many covering space semigroups with \(B\) as a boundary, and each of them is a retract of \(B\).
reviewed by: Kateryna Pavlyk
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 54C15
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 55R10
Mathematics Subject Classification ID: 57M10
zbMATH DE Number: 6680056
zbMATH Keywords: topological group
zbMATH Keywords: compact topological semigroup
zbMATH Keywords: retract
zbMATH Keywords: mapping cylinder
zbMATH Keywords: covering space
zbMATH Keywords: fibre bundle
zbMATH Keywords: torus knot
Wikidata QID: Q115389987
MaRDI profile type: Publication
full work available at URL: s00022-016-0318-2
OpenAlex ID: W2287820326
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DOI: 10.1007/S00022-016-0318-2
description: scientific article; zbMATH DE number 6680056