Principal bundles on two-dimensional CW-complexes with disconnected structure group

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Oliveira, AG (Author) FCUP

Journal

Title: Glasgow Mathematical Journal

Vol. 64

Pages: 675-690

ISSN: 0017-0895

Publisher: Cambridge University Press

Indexing

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Other information

Authenticus ID: P-00V-XDJ

DOI: 10.1017/s0017089521000434

Abstract (EN): Given any topological group G, the topological classification of principal G-bundles over a finite CW-complex X is long known to be given by the set of free homotopy classes of maps from X to the corresponding classifying space BG. This classical result has been long-used to provide such classification in terms of explicit characteristic classes. However, even when X has dimension 2, there is a case in which such explicit classification has not been explicitly considered. This is the case where G is a Lie group, whose group of components acts nontrivially on its fundamental group pi(1)G. Here, we deal with this case and obtain the classification, in terms of characteristic classes, of principal G-bundles over a finite CW-complex of dimension 2, with G is a Lie group such that pi(0)G is abelian.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16