Compact flat manifolds with holonomy group \(\mathbb Z_2\oplus\mathbb Z_2\). II
The classification of compact flat manifolds (up to affine equivalence) is equivalent, after Bieberbach's results, to the classification of their fundamental groups (up to isomorphism). In this paper the authors give a complete classification of compact flat manifolds with holonomy group \({\mathbb Z}_2\oplus{\mathbb Z}_2\), with the property that the holonomy representation is a direct sum of \({\mathbb Z}_2\oplus{\mathbb Z}_2\)-indecomposable representations of \({\mathbb Z}\)-rank equal to 1 or 2. The compact flat manifolds in this class which have first Betti number zero are exactly those considered in [the authors, Proc. Am. Math. Soc. 124, No. 8, 2491--2499 (1996; Zbl 0864.53027)].
scientific article; zbMATH DE number 1319597
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