Geodesic
Principal bundles on two-dimensional CW-complexes with disconnected structure group
Glasgow mathematical journal, Tome 64 (2022) no. 3, pp. 675-690

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DOI

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.
DOI : 10.1017/S0017089521000434
Mots-clés : Principal bundles, characteristic classes, CW-complexes 
Oliveira, André G. Principal bundles on two-dimensional CW-complexes with disconnected structure group. Glasgow mathematical journal, Tome 64 (2022) no. 3, pp. 675-690. doi: 10.1017/S0017089521000434
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     author = {Oliveira, Andr\'e G.},
     title = {Principal bundles on two-dimensional {CW-complexes} with disconnected structure group},
     journal = {Glasgow mathematical journal},
     pages = {675--690},
     year = {2022},
     volume = {64},
     number = {3},
     doi = {10.1017/S0017089521000434},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000434/}
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