Topological invariants of principal \(G\)-bundles with singularities
type: Item
instance of: scholarly article
title: Topological invariants of principal \(G\)-bundles with singularities
zbMATH Open document ID: 1407.57026
DOI: 10.1134/S1995080218050013
author: F. A. Arias Amaya
author: M. A. Malakhaltsev
published in: Lobachevskii Journal of Mathematics
publication date: 2018-09-27T00:00:00Z
review text: A principal \(G\)-bundle with singularities is a principal bundle \(\pi : \overline{P} \rightarrow M\) with structure group \(\overline{G}\) which reduces to a subgroup \(G \subset \overline{G}\) on the set \(M \setminus \Sigma\), where \(M\) is a compact \(n\)-dimensional manifold and \(\Sigma \subset M\) is a \(k\)-dimensional submanifold. This paper constructs topological invariants for principal bundles with singularities. This is done by applying obstruction theory to the section \(M \rightarrow \overline{P}/G\) corresponding to the reduction to obtain a topological invariant in \(H^{n-k}(M, M \setminus \Sigma; \pi_{n-k-1}(\overline{G}/G))\)
Mathematics Subject Classification ID: 57R91
Mathematics Subject Classification ID: 55R55
zbMATH DE Number: 6945059
zbMATH Keywords: \(G\)-structure
zbMATH Keywords: principal bundle with singularities
zbMATH Keywords: obstruction
zbMATH Keywords: singularity of \(G\)-structure
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
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full work available at URL: s1995080218050013
OpenAlex ID: W2842373259
Wikidata QID: Q129581867
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description: scientific article; zbMATH DE number 6945059