1 results
Principal bundles on two-dimensional CW-complexes with disconnected structure group
- Part of
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- Journal:
- Glasgow Mathematical Journal / Volume 64 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 06 January 2022, pp. 675-690
- Print publication:
- September 2022
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- Article
- Export citation
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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
$\pi_1G$
. 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 
$\pi_0G$
is abelian.
