Cohomological rigidity of oriented Hantzsche-Wendt manifolds

By Hantzsche-Wendt manifold (for short HW-manifold) we understand any oriented closed Riemannian manifold of dimension n with a holonomy group (Z2)n−1. Two HW-manifolds M1 and M2 are cohomological rigid if and only if a homeomorphism between M1 and M2 is equivalent to an isomorphism of graded rings H⁎(M1,F2) and H⁎(M2,F2). We prove that HW-manifolds are cohomological rigid.