Cohomological rigidity of oriented Hantzsche-Wendt manidolds

TL;DR

This paper proves that oriented Hantzsche-Wendt manifolds are uniquely determined by their cohomology rings over F_2, establishing their cohomological rigidity.

Contribution

It demonstrates that HW-manifolds are cohomologically rigid, meaning their topological type is fully determined by their cohomology ring over F_2.

Findings

HW-manifolds are cohomologically rigid

Cohomology ring over F_2 determines HW-manifolds up to homeomorphism

Provides a new rigidity result for a class of flat manifolds

Abstract

By Hantzsche-Wendt manifold (for short HW-manifold) we understand any oriented closed Riemannian manifold of dimension n with a holonomy group (Z_2)^{n-1}. Two HW-manifolds M_1 and M_2 are cohomological rigid if and only if a homeomorphism between M_1 and M_2 is equivalent to an isomorphism of graded rings H^{*}(M_1,F_2) and H^{*}(M_2,F_2). We prove that HW-manifolds are cohomological rigid.