A model for embedding finite coverings defined by principal bundles into bundles of manifolds
type: Item
instance of: scholarly article
title: A model for embedding finite coverings defined by principal bundles into bundles of manifolds
zbMATH Open document ID: 0644.57009
DOI: 10.1016/0166-8641(88)90030-2
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: For any given finite group G and locally trivial fibration \(p: V\to X\) over a connected CW-complex with connected manifold of dimension \(\geq 2\) as fiber, a principal G-bundle \(P_ G: F_ G(V)\to C_ G(V)\) is constructed along with a locally trivial fibration \(p_ C: C_ G(V)\to X\). It is then shown that the sections of \(p_ C\) classify, via pullback of \(p_ G\), those principal G-bundles on X that admit an embedding into \(p: V\to X\). A special case of this construction (when p is the trivial complex line bundle) yields a classification of polynomial principal G- bundles. An algebraic characterization of such G-bundles is also given in terms of homomorphisms into braid groups.
Mathematics Subject Classification ID: 57R22
Mathematics Subject Classification ID: 55R15
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N35
zbMATH DE Number: 4050556
zbMATH Keywords: fibrewise embedding
zbMATH Keywords: polynomial covering map
zbMATH Keywords: G-configuration
zbMATH Keywords: embedding finite coverings
zbMATH Keywords: locally trivial fibration
zbMATH Keywords: principal G-bundle
zbMATH Keywords: polynomial principal G-bundles
zbMATH Keywords: homomorphisms into braid groups
author: Vagn Lundsgaard Hansen
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90030-2
OpenAlex ID: W1986446996
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description: scientific article; zbMATH DE number 4050556