We prove that the existence of a Spin-structure on an oriented real vector bundle and the number of them can be obtained in terms of 2-fold coverings of the total space of the SO(n)-principal bundle associated to the vector bundle. Basically we use theory of covering spaces. We give a few elementary applications making clear that the Spin-bundle associated to a Spin-structure is not suffcient to classify such structure, as pointed out by [6].
@article{7451,
title = {Spin-structures and 2-fold coverings - doi: 10.5269/bspm.v23i1-2.7451},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v23i1-2.7451},
language = {EN},
url = {http://dml.mathdoc.fr/item/7451}
}
Gonçalves, Daciberg L.; Hayat, Claude; Mello, Maria Hermínia P. L. Spin-structures and 2-fold coverings - doi: 10.5269/bspm.v23i1-2.7451. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v23i1-2.7451. http://gdmltest.u-ga.fr/item/7451/