<b>Spin-structures and 2-fold coverings</b> - doi: 10.5269/bspm.v23i1-2.7451

Abstract

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].