Spin structures on flat manifolds (Q5919745)

Let \(M\) be a flat manifold, i.e. a compact, Riemannian manifold without boundary, with sectional curvature equal to zero. From the Bieberbach theorems there exists only a finite number of such objects of a given dimension, up to affine diffeomorphism. The authors present an algorithmic approach to the problem of the existence of spin structures on flat manifolds. Using this they make a complete classification of the existence of such structures on flat manifolds of dimensions 5 and 6. We should mention that the computer program CARAT is used.